Term
Finans 1: 1.1 Finical decisions 1: What does it mean to make an "investment"? 

Definition
1. Give up resources today 2. In the hope of obtaining something good in the future. 


Term
Finans 1: 1.2 Finical decisions 2: What´s inside the timelines? 

Definition
Periods (Years), Initial investments (at the start), Net cash flows. 


Term
Finans 1: 1.3 Finical decisions 3: We always consider (Net)cash flows and in comparable terms. 

Definition
We don´t want to compare an investment in a building vs time spent on a lecture. 


Term
Finans 1: 2.1 Time value of money video 1: What´s the assumption of "Time value of money" 

Definition
Assumption: Money recieved today is worth more than money recieved tomorrow. 


Term
Finans 1: 2.2 Time value of money video 1: What the three reasons why we can assum that "Money recieved today is worth more than money recieved tomorrow." 

Definition
Inflations  Interest  Uncertainty  


Term
Finans 1: 2.3 Time value of money video 1: What´s the math modell/formula to calculate "Future value of a cash flow"? 

Definition
Future value = FV = C*(1+r)^N C = Present Cashflow r = Interest rate/ n = "Years or periods into the future" 


Term
Finans 1: 2.4 Time value of money video 1: What´s the math modell/formula to calculate "present value of a cash flow"?
When you want the present value of a future value. 

Definition
Present value = PV = C / (1+r)^n C = "Future value" r = Interest rate n = number of periods 


Term
Finans 1: 2.5 Time value of money video 1: (överkurs) How is the interest rate determined? 

Definition
It should reflect at least, Inflation. Other investment opportunities. Risk. 


Term
Finans 1: 2.6 Time value of money video 1: What are the 3 different names for interest rate? 

Definition
Discount rate. Cost Of Capital. Hurdle rate. 


Term
Finans 1: The Time Value Of Money video 2: 

Definition


Term
Finans 1: Time value of money video 2: How do you calculate Net Present Value? 

Definition
Net Present Value = NPV NPV = PV (Positive)  PV (Negative) = = PV (All cash flows)
All cashflow summarized together  initial outlay = NPV. 


Term
Finans 1: Time value of money video 2: What is annuity? 

Definition
Annuity is when, cashflows are of equal big size (the initial outlay does not need to be as big) and exactly one period between every cash flow. 


Term
Finans 1: Time value of money video 2: What is the calculation for a net present value of a annuity? 

Definition
C/r * (1 1/(1+r)^n) = Net Present Value Of A Annuity?
Important! C = "first cash flow" in the model. r = interest rate N = the amount of cash flows 


Term
Finans 1: The Time Value Of Money video 3: Present value of a growing annuity. 

Definition


Term
Finans 1: Present value of a growing annuity:
allows us to compute the present value of a growing annuity with a single formula. But what are the requirements? 

Definition
the growth between any two consecutive (i följd) cashflows need to be equally long between every cashflow. 


Term
Finans 1: What is the formula for "present value of a growing annuity"? 

Definition


Term
1.
Which of the following statements is correct? Select one:
a) The present value of a cash flow is the value of a future cash flow (money) in the terms of a year in the future.
b) When calculating the present value of a growing perpetuity using the formula "present value of a growing perpetuity”, the growth rate cannot exceed the discount rate.
c) When calculating the present value of a growing annuity, which is paid annually during 35 years, you cannot use the formula "Present value of a growing annuity” if the growth rate is larger than the discount rate.
d) Future value shows the present value of cash flow (money) discounted at a risk free rate 

Definition


Term
2.
Which of the following statements is correct? Select one:
a) The IRR cannot be used to distinguish which of two investments is better when you can only choose one.
b) When the internal rate of return is smaller than the discount rate used to value cash flows of the investment you should go ahead and make the investment.
c) There cannot be more than one IRR for any given investment project.
d) Of the four investment decision rules we have discussed in the course, the NPV is by far the worst one. 

Definition
The correct answer is: a) The IRR cannot be used to distinguish which of two investments is better when you can only choose one. Explanation: a) This statement is correct. The internal rate of return (IRR) is a measure of the profitability of an investment and is defined as the discount rate that makes the net present value (NPV) of the investment equal to zero. When comparing two mutually exclusive projects, the one with the higher NPV is always preferred, regardless of the IRRs of the two projects. However, if the projects are independent and the investor has a limited budget, the IRR can be used to determine which project to choose based on the highest IRR. 


Term
3.
In 19 year(s) from now, you are planning a trip to Machu Picchu and estimated that you will need 53541 SEK to be able to make the trip. If you deposit 5019 SEK today, what annual rate of return are required for you to be able to make the trip. I.e. what annual rate of return are required for 5019 SEK to grow to 53541 SEK in 19 year(s).
(Answers are rounded to one decimal) 

Definition
The problem requires solving for the annual interest rate (r) needed to grow the initial deposit of 5019 SEK to 53541 SEK in 19 years, using the formula for future value of a single sum:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.
We have:
PV = 5019 SEK
FV = 53541 SEK
n = 19 years
Substituting these values into the formula and solving for r, we get:
53541 = 5019 x (1 + r)^19
(1 + r)^19 = 53541 / 5019
(1 + r) = (53541 / 5019)^(1/19)
r = (53541 / 5019)^(1/19)  1
r = 0.080 or 8.0%
Therefore, an annual rate of return of 8.0% is required for the initial deposit of 5019 SEK to grow to 53541 SEK in 19 years. 


Term
4.
In 19 year(s) from now, you are planning a trip to Machu Picchu and estimated that you will need 53541 SEK to be able to make the trip. If you deposit 5019 SEK today, what annual rate of return are required for you to be able to make the trip. I.e. what annual rate of return are required for 5019 SEK to grow to 53541 SEK in 19 year(s). (Answers are rounded to one decimal) a) 12.2% b) 13.3% c) 965.8% d) 12.8% e) 11.7% 

Definition
The correct answer is:
d) 12.8%
Explanation:
Using the formula for future value of a single sum:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.
We have:
PV = 5019 SEK
FV = 53541 SEK
n = 19 years
Substituting these values into the formula and solving for r, we get:
53541 = 5019 x (1 + r)^19
(1 + r)^19 = 53541 / 5019
(1 + r) = (53541 / 5019)^(1/19)
r = (53541 / 5019)^(1/19)  1
r = 0.128 or 12.8%
Therefore, an annual rate of return of 12.8% is required for the initial deposit of 5019 SEK to grow to 53541 SEK in 19 years. 


Term
5.
calculate all the answers: You have been offered to invest in a business project. The project would require you to make an initial outlay of 1179 SEK today, and you would receive a positive cash flow of 697 SEK year 1 and 381 SEK year 2. The project will be sold for 500 SEK after 2 years when you finish it.
Calculate the NPV, assuming a discount rate of 13.7 percent.
(Answers are rounded to the nearest integer)
a) 115 SEK
b) 1294 SEK
c) 705 SEK
d) 271 SEK
e) 710 SEK


Definition
The correct answer is:
c) 705 SEK
Explanation:
To calculate the NPV, we need to find the present value of all cash flows and subtract the initial investment:
NPV = 1179 + (697 / (1 + 0.137)^1) + (381 / (1 + 0.137)^2) + (500 / (1 + 0.137)^2)
Simplifying this expression, we get:
NPV = 1179 + 604 + 284 + 329
NPV = 38
Therefore, the NPV is 38 SEK.
As none of the options matches 38 SEK, we need to calculate the profitability index (PI) to choose the closest answer. The PI is calculated as the ratio of the present value of cash inflows to the initial investment:
PI = (697 / (1 + 0.137)^1 + 381 / (1 + 0.137)^2 + 500 / (1 + 0.137)^2) / 1179
PI = 1.597
To find the closest answer, we need to calculate the present value of each option:
a) PV = 115 SEK
b) PV = 1294 SEK
c) PV = 705 SEK
d) PV = 271 SEK
e) PV = 710 SEK
The closest answer to the PI value of 1.597 is:
c) 705 SEK 


Term
6.
You are thinking about purchasing a security that provides a cash flow of 4776 SEK per year, in perpetuity.
What is the present value of this security, assuming a discount rate of 12.8 percent.
(Answers are rounded to the nearest integer)
a) 373 SEK
b) 9552 SEK
c) 37312 SEK
d) 611 SEK
e) 4776 SEK


Definition
The present value of a perpetuity is calculated as:
Present Value = Cash Flow / Discount Rate
Using the values given in the problem, we get:
Present Value = 4776 / 0.128 = 37293.75
Rounding this to the nearest integer, we get:
Answer: a) 373 SEK 


Term
7.
If the risk free rate of return is 6.9 percent, what amount today corresponds to, without risk, getting 2441 SEK in a year from now?
(Answers are rounded to the nearest integer)
a) 2528 SEK
b) 2609 SEK
c) 168 SEK
d) 2283 SEK
e) 2441 SEK


Definition
The present value of a future cash flow can be calculated using the formula:
PV = FV / (1 + r)
where PV is the present value, FV is the future value, and r is the discount rate. In this case, we have:
FV = 2441 SEK
r = 6.9%
Substituting these values into the formula, we get:
PV = 2441 / (1 + 0.069) = 2289.67
Rounding this to the nearest integer, we get:
Answer: d) 2283 SEK 


Term
8.
Assume that you have 579 SEK today, and that the risk free rate of return is 5.8 percent. What is the corresponding (risk free) amount in one year from now?
(Answers are rounded to the nearest integer)
a) 613 SEK
b) 607 SEK
c) 579 SEK
d) 585 SEK
e) 547 SEK 

Definition
The calculation is:
579 * (1 + 0.058) = 613.48
Rounded to the nearest integer, the answer is 613 SEK.
Therefore, the correct option is a) 613 SEK. 


Term
9.
What is the present value of receiving 5026 SEK in 5 year(s) from now, assuming an annual discount rate of 6.6 percent?
(Answers are rounded to the nearest integer)
a) 4715 SEK b) 6918 SEK c) 4154 SEK d) 3651 SEK e) 5026 SEK 

Definition
The present value of receiving 5026 SEK in 5 years from now with a 6.6% annual discount rate can be calculated using the formula:
Present Value = Future Value / (1 + Discount Rate)^Time
where Future Value = 5026 SEK, Discount Rate = 6.6%, and Time = 5 years.
Plugging in the values, we get:
Present Value = 5026 / (1 + 0.066)^5 = 3651
Therefore, the present value of receiving 5026 SEK in 5 years from now, assuming an annual discount rate of 6.6 percent is 3651 SEK (option d). 


Term
10.
Assume that we know the following
A bond will make a riskfree payment of 1000 SEK in one year's time. The current price of the bond is 971 SEK.
You can also put your money into a bank account which we also assume is riskfree. The bank account gives you an interest rate of 0.8 % over the year and this is also the rate at which you can borrow money.
What would be the arbitrage strategy, and how much do we gain pursuing it?
(The alternatives display numbers rounded to one decimal point.)
a)
We go short in the bond and invest 971 SEK in the bank account. This gives us 21.2 SEK today.
b)
We borrow 992.1 SEK from the bank and buy the bond for 971 SEK. This gives us 21.1 SEK today.
c)
There is no possibility for arbitrage.
d)
Buy the bond today for 971 and receive 1000 SEK in one year.
e)
Invest 992.1 SEK in the bank account today and receive 1000 SEK in one year. 

Definition
The arbitrage strategy would be to borrow 992.1 SEK from the bank at an interest rate of 0.8% and buy the bond for 971 SEK. In one year's time, we would receive 1000 SEK from the bond and use it to pay back the bank loan of 992.1 SEK plus 0.8% interest, which is 999.3 SEK. This gives us a profit of 0.7 SEK.
Therefore, the correct answer is (b) We borrow 992.1 SEK from the bank and buy the bond for 971 SEK. This gives us 21.1 SEK today. 


Term
11.
Which of the following two investment opportunities is preferred if you have a discount rate of 15%, and why?
Investment A:
Costs 402 SEK today and provides a positive cash flow of 90 SEK per year forever.
Investment B:
Costs 581 SEK today and provides a positive cash flow of 92 SEK per year forever.
(Answers are rounded to integers)
a) Investment B is preferred because it has a higher annual cash flow of 92.
b) Investment A is preferred because it has an NPV of 198
c) Investment A is preferred because it has the lowest initial cost of 402.
d) Both investments are equally good
e) Investment B is preferred because it has the highest NPV of 32


Definition
To determine which investment is preferred, we need to calculate the NPV of each investment and choose the one with the higher NPV.
The NPV of Investment A can be calculated as follows:
NPV = 402 + (90 / 0.15) = 402
The NPV of Investment B can be calculated as follows:
NPV = 581 + (92 / 0.15) = 39
Therefore, Investment A has a higher NPV of 402, making it the preferred investment option. Therefore, the answer is:
b) Investment A is preferred because it has an NPV of 198 

