Question

1. You invest £150,000 and receive £10,000 in year 1; £20,000 in year 2; £30,000 in year 3; and a perpetuity of £10,000 each year from year 4 onwards. The risk free rate is 5% and the average return on the market index is 10%. The beta of the project is 0.8. Is the project desirable?

2. Suppose that the perpetuity in the question above ends in year 20. Is the project desirable now?

3. You are the chairman of the board for the company that is planning the investment, and you suspect that the project is a “pet project” for your manager. Your experience is that the manager has been very keen to get approval from the board for going ahead. How would you interpret this piece of information? How could you evaluate the project’s chances of success in ways other than a NPV estimate as above? How could the manager convince you that the project is “really” worth while?

Answer 1

The net present value in the 1st case has been calculated as follows

NPV = sum of present value of cash inflows from year 1 to 3- initial investment + present value of cash inflows starting 4th year and beyond

NPV in the case where the perpetuity stops at 20th year:

the perpetuity will last for a period of 17 years in total ( from year 4 to year 20)

since the perpetuity is basically an annuity of an amount of 1000 for a period of 17 years

Present value of cash inflows from 4th year to 20th year = 1000*PVIFA

PVIFA = present value interest rate factor of annuity

PVIFA = ((1+r)ⁿ)-1)/((1+r)ⁿ *r)

where; r = required return for project

n = period of perpetuity = 17 years

formula used for 1)

NPV = [[10000/(1+r)]+ [20000/(1+r)²]+ [30000/(1+r)³]+ [10000/(r*(1+r)³]]-150000

where; r = required return for project = 9% = 0.09