1. Fundamentals of Finance
Pre-Master
Nguyen Manh Hiep - Nicolas Taillet

2. Chapter 3. The Time Value of Money and Financial Decision Making
Fundamentals of Finance
Pre-Master
Chapter 3. The Time Value of Money and Financial Decision Making
Nguyen Manh Hiep

3. Content
The Time Value of Money
NPV and IRR
Fun Quiz

4. I – The Time Value of Money
Interpretation of Interest Rate
A dollar on hand is preferred to a dollar received in the future (it’s an assumption).
To induce people to invest their money, investments must offer additional benefit (i.e., risk free rate).
Investments are risky. Minor additional benefit is not enough. There must be a risk premium.

5. I – The Time Value of Money
Interpretation of Interest Rate
Interest Rate [or (Required) Rate of Return]
= Risk Free Rate
+ Risk Premium
(+ Inflation Premium)
Risk free rate: Preference for cash on hand versus future income.

6. I – The Time Value of Money
Interpretation of Interest Rate
Inflation premium: maintain the same level of purchasing power.
Risk free rate + risk premium: increase in purchasing power.
Given expected cash-flow from the assets, determining the rate of returns is the same as setting the price.

7. I – The Time Value of Money
Interpretation of Interest Rate
Each individual requires different rate of returns on the same assets, based on their level of risk tolerance. Highly risk-adverse investors required higher returns.
However, many financial assets are traded in the markets. Their prices (and rates of return) are set at the equilibrium of demands and supplies or at arbitrage-free prices. The rates of return set by the market are called the market rates of return.

8. I – The Time Value of Money
Formula Summary

9. I – The Time Value of Money
Compounding n 1 2 3 …
n-1 PV
FVn
Compounding is the process of calculating future value from present value.
Future value is the amount of money an investment will grow to at some date in the future by earning interest at some compound rate.

10. I – The Time Value of Money
Example: Sophie deposits $1.000 into a one-year savings account earning an interest rate of 10%.
How much does she have at the end of the 1st year?
Sophie is absent-minded and forgets about the savings account. At the end of the third year she suddenly recalls. Assuming that interest rate doesn’t change, how much can she withdraw from her account?
What if Sophie deposited Euro 1,000 into a six- month savings account earning an interest rate of 10%?

11. I – The Time Value of Money
Example: Sophie has been depositing Euro 500 into a savings account on every birthdays since her son Nicolas was born. The interest rate is 10%, compounded annually. How much money will be in the account on Nicolas’ 20th birthday immediately before Sophie makes the deposit on that day?
Assume that the amount deposited increases by 5% each year. How much money will be in the account on Nicolas’ 20th birthday immediately before Sophie makes the deposit on that day?

12. I – The Time Value of Money
Discounting n 1 2 3 …
n-1 PV
FVn
Discounting is the process of calculating the present value future cash flows.

13. I – The Time Value of Money
Example: Sophie divorces her husband Nicolas on Jan Their marital property is a house worth Euro 1 million, to be divided equally between them. They have agreed that Nicolas keeps the house, and pay Sophie Euro 500 in one year.
Assuming no risk, and the interest rate on one- year savings account is 10%. What is the present value of Sophie’s money?
Assuming they have agreed that Nicolas will pay Sophie 100k now, and the rest in four equal installments in the next 4 years. What is the present value of Sophie’s payments?

14. I – The Time Value of Money
Example: A 5-year-to-maturity coupon bond is trading at 10% market interest rate. Coupons are paid annually at the coupon rate of 10%. Calculate the price of the bond.
Now suppose that the market rate is 8% (12%), recalculate the price of the bond.
Example: A 10%-coupon, perpetual bond is currently traded at the market interest rate of 12%. Calculate the price of the bond.

15. I – The Time Value of Money
Arbitrage, an Example
Suppose there is no risk.
A 1-year-to maturity, discount bond is selling at 94. Calculate the market rate.
Bank lending and deposit rate are both 5%. Is there an opportunity to earn money?
Now suppose instead that the bond is selling at 96. Calculate the interest rate and identify the arbitrage opportunity.

16. I – The Time Value of Money
Example: Nicolas is considering taking a 3-year loan of euro 1 million to expand his business. Sophie, a loan officer at Agrobanco, offers him the loan at 12% interest rate. Suppose that the loan is to be repaid by 3 equal payments made at the end of each year. Calculate the payment.
Suppose that the loan is to be repaid in 36 equal monthly payments at the end of each month. Calculate the payment.

17. II – NPV and IRR
Net present value (NPV) of an investment is the present value of its expected cash inflows minus the present value of its expected cash outflows.
Accept those projects with positive NPV.
When choosing among mutually exclusive projects, choose the one (or the combination of ones) with highest NPV.

18. II – NPV and IRR
The internal rate of return (IRR) is defined as the rate of return that equates the PV of an investment’s expected benefits with the PV of its costs.
Accept those projects with IRR higher than the cost of capital.
Always prioritize NPV over IRR in decision making.

19. II – NPV and IRR
Example: Nicolas is considering a 5-year project which requires an initial investment outlay of euro 10 million. Nicolas estimates that it will generate a cash inflow of euro 2.5 million at the end of the first year, which will grow at an annual rate of 10% in the next 4 years. At the end of the project, Nicolas estimates that plant and equipment can be sold for a salvage value of 0.5 million. Nicolas estimates that the cost of capital is 15%. Calculate NPV and IRR. Should Nicolas accept or reject the project?

20. II – NPV and IRR Example: Nicolas Corp. Projects
If Nicolas has euro 20 million.
If Nicolas has euro 25 or 30 million and can (can not) invest in a portion of the projects.
If Nicolas has euro 10 billion and can postpone the project until next year.
Project 1 2
NPV
@10%
IRR A
-20 30 B
-10 5 C -5 15 10

21. III – Fun Quiz What is Price
Nicolas receives a free, super-quality, non-stick pan from BigPan Supermarket as part of a promotion program for loyal customers. Identical pans are currently selling at euro 80 in every supermarket. Nicolas’ grand-mother offers to buy it from him at euro 20. What is the price of the pan?
Euro 0.
Euro 20
Euro 80.

22. III – Fun Quiz Arbitrage in an Imperfect Market
$1000 par 1-year discount note.
Bank deposit interest rate 6%.
Bank loan rate 6.5%.
What happens if note price higher than $ or lower than $938.97?
What happens if note price is between $ and $943.4?

23. III – Fun Quiz The Law of One Price and Asset Valuation
Stock A: current market price $100, expected to be $140 in 1 year if the economy is good (prob. 50%) or $80 in case of downturn (50%).
Stock B: price in 1 year is expected to be $60 in case of good economic condition and $0 in case of downturn.
One-year treasury bill market rate 4%.
What should be the current market price of stock B if the Law of One Price holds?

24. III – Fun Quiz The Law of One Price and Asset Valuation
Stock A: current market price $100, expected to be $140 in 1 year if the economy is good (prob. 50%) or $80 in case of downturn (50%).
Stock B: price in 1 year is expected to be $0 in case of good economic condition and $60 in case of downturn.
One-year treasury bill market rate 4%.
What should be the current market price of stock B if the Law of One Price holds?

25. END OF CHAPTER 4