Question

A small restaurant costs 350,000. Expected profits equal 22000/year for six years when value is 400000. What is the projects rate of return?

Please show me the equation being used, can't use excel during the test! Thank You

Answer 1

Given

Initial investment = 350,000

Expected annual profit = 22,000

Salvage (terminal value) = 400,000

Life = 6 years

What is the rate of return?

Calculating the rate of return by using the trial and error method

Let the rate of interest is 10%

At 10% calculate the Net Present Value

NPV = -350,000 + 22,000 (P/A, 10%, 6) + 400,000 (P/F, 10%, 6)

NPV = -350,000 + 22,000 (4.3553) + 400,000 (0.5645) = -28,383

We can see that the NPV is negative. Now decrease the rate of interest to get a positive NPW.

Let the rate of interest decreased to 8%

NPV at 8 %

PV = -350,000 + 22,000 (P/A, 8%, 6) + 400,000 (P/F, 8%, 6)

PV = -350,000 + 22,000 (4.6229) + 400,000 (0.6302) = 3,784

Now use interpolation to calculate the rate of return.

Using interpolation

Rate of return = 8% + [3,784 – 0 ÷ 3,784 – (-28,383)]*2% = 8.23%

Rate of return will be 8.23%