Question

Consider a company considering a project that will last three years

A. If the project will return $30 million a year for the next three years and the cost interest rate is 8%, what is the value of these cash flows?

B. Suppose instead the project will return $20 million at the end of the first year and at the end of the second year, and $40 million at the end of the third year. No other be Guaranteed. If the opportunity cost interest rate is 8%. What is the value of these cash flows?

C. Why are the values of the cash flows different even though there is a total amount being guaranteed in both projects?

EXPLAIN YOUR ANSWERS

Answer 1

A.

Cash flows per year = $30 Million

R = 8%

n = 3 years

Present value of the cash flows = 30*(1-1/(1+R)^n)/R = 30*(1-1/1.08^3)/.08

Present value of the cash flows = $77.31 Million

B.

When for year 1 and 2, the cash flows are $20 Million each and $40 million in year 3,

Present value of the cash flows = 20/1.08 + 20/1.08^2 + 40/1.08^3

Present value of the cash flows = $67.42 Million

C.

Difference is due to the following reasons:

1. first case, there is a total of $90 Million in 3 years and in second case, it is total of $80 millions in 3 years. So, there will difference in final value.

2. In first case there is uniformity in cash flows per year, but in second case biggest cash flow comes in the last 3rd year. It makes a bigger discounting to the biggest cash flow, causing reduced present value of the total cash flows. It makes a big difference.