Question

4.19 A 7-year project requires an initial cash injection of $10,000. Expenses of $500 are incurred at the end of every year. The project starts to generate income of $3,000 after 3 years, and the income increases at a rate of 10% every year.

(a) Calculate the yield rate of the project.

(b) Repeat (a), assuming that at the end of each year, the company has to pay 5% tax on investment income after expenses. (If the net income in the year is negative, no tax is paid.) Compare your answer with that obtained in (a).

Answer 1

a. The cash flows of the different years will look like:

Year 0: -10000

Year 1,2: -500

Year 3: 3000 - 500 = 2500

Year 4: 3000 x 1.1 - 500 = 2800

Year 5: 3000 x 1.1^2 - 500 = 3130

Year 6: 3000 x 1.1^3 - 500 = 3493

Year 7: 3000 x 1.1^4 - 500 = 3892.3

So, writing the PV equation, we have:

-10000 = -500/(1+R) - 500/(1+R)^2 + 2500/(1+R)^3 + 2800/(1+R)^4 + 3130/(1+R)^5 + 3493/(1+R)^6 + 3892.3/(1+R)^7

Hence, R = 7.502%.

b. Now, the cash flows will change slightly:

Year 0: -10000

Year 1,2: -500

Year 3: 2500 x 0.95 = 2375

Year 4: 2800 x 0.95 = 2660

Year 5: 3130 x 0.95 = 2973.5

Year 6: 3493 x 0.95 = 3318.35

Year 7: 3892.3 x 0.95 = 3697.685

So, writing the PV equation, we have:

-10000 = -500/(1+R) - 500/(1+R)^2 + 2375/(1+R)^3 + 2660/(1+R)^4 + 2973.5/(1+R)^5 + 3318.35/(1+R)^6 + 3697.685/(1+R)^7

Hence, R = 6.397%

We see that as the tax payments are introduced, the yield becomes less as some of our income is going in paying taxes.