Basic Principles of Valuation – Answer Key

Tutorial 1 – Basic Principles of Valuation – Answer Key

Question 1:

1. Explain the relationships between Present Value, Discount Factor, Discount Rate and Net Present Value.
   The Present Value is the value of all future cash flows generated by the investment at time 0.  The cash flows are discounted by dividing the future payments with (1+ the Discount Rate)n, where n is the number of years of discounting.
   The Discount Factor is the inverse of (1 + the Discount Rate)n: DF = 1/(1+DR)n.  The Net Present Value subtracts the initial investment from the Present Value of the investment.
2. What is the Net Present Value rule?
   The Net Present Value rule states that you should accept all investments with a positive Net Present Value.
3. Why is a pound today worth more than a pound tomorrow?
   A pound today is worth more than a pound tomorrow because if you had the pound today you could invest it, in let’s say a risk-free bank account, and receive the pound plus the interest tomorrow.
4. If the return of an investment is lower than the discount rate, is the Present Value positive or negative?
   As long as the cash flows generated by the investment (ignoring the initial investment itself) are positive, the Present Value will be positive.  The sign of the NPV will however be dictated by the relationship between the return and the discount rate.  Specifically a return < discount rate will generate a negative NPV.
5. Explain why the discount rate equals the opportunity cost of capital.
   The discount rate equals the opportunity cost of capital because it represents the alternative return you could get on a project of the same risk.  Let’s say you face a risk-free investment in a project.  Instead of investing in the project you could invest the money in government bonds.  In choosing between the two investment opportunities, you will discount the cash flows of the investment with (1+ the return on government bonds).  You can then use the Net Present Value rule to determine whether to accept the project or not.

Question 2:

Calculate the NPV and rate of return for each of the following investments.  The opportunity cost of capital is 15% for all four investments.

1. Which investment is most valuable?

We’ll start by calculating NPV and ROI for every investment opportunity: for each investment:

[pic 1];                                  [pic 2] 

[pic 3]

Investment 1 gives the highest NPV, whereas investment 4 gives the highest relative return on the investment.  Assuming that these projects can be replicated, you should take as many of investment 4 (e.g. buying shares) as your capital access will allow.  If you can’t replicate the investments, you should take investment 1, 2 and 4 since they all give positive NPV’s (remember the NPV rule.)  If you only have 10,000 available (and it is not possible to borrow money) you should take project 2 and 4, and put the remaining 3,000 in the bank.