Question

A company project has an initial cost of $40,000, expected net cash flows of $9,000 per year for 7 years. The company has a target capital structure of 10% short term debt at an           interest rate of 6.0%, 50% long term debt at an interest rate of 9.0%, and 40% equity with a cost of 18%. The company’s tax rate is 28%.

            a.         What is the projects DPB?

Answer 1

present value factor = 1/(1+r)^n

here,

r = WACC.

WACC is to be found out:

after tax cost of short term debt = before tax cost *(1-tax rate) =>6%*(1-0.28)

=>4.32%.

after tax cost of longterm debt = before tax cost*(1-tax cost) =>9%*(1-0.28)

=>6.48%.

now WACC:

=>(0.10 short term debt * 4.32) + (0.50 long term debt * 6.48) + (0.40*18)

=>0.432+3.24+7.20

=>10.872%.

now,

discounted payback period:

investment to be recovered:

year	cash flow	present value factor	cash flow* present value factor	accumulated cash flow
1	9000	1/(1.10872)^1=>0.90194	9000*0.90194 =>8,117.46	8,117.46
2	9000	1/(1.10872)^2=>0.81350	9000*0.81350=>7,321.50	15,438.96
3	9000	1/(1.10872)^3=>0.73373	9000*0.73373=>6,603.57	15438.96+6603.57=>22,042.53
4	9000	1/(1.10872)^4=>0.66178	9000*0.66178=>5,956.02	22042.53+5956.02=>27,998.55
5	9000	1/(1.10872)^5=>0.59688	9000*0.59688=>5,371.92	27,998.55+5371.92=>33,370.47
6	9000	1/(1.10872)^6=>0.53835	9000*0.53835=>4,845.15	33,370.47+4845.15=>38,215.62
7	9000	1/(1.10872)^7=>0.48556	9000*0.48556=>4,370.04	38,215.62+4370.04=>42,585.66

the amount of $40,000 is recovered between 6 th and 7 year.

discounted payback period = 6 years + (40,000-38,215.62) / (42,585.66-38,215.62)

=>6 years +(1784.38/4370.04)

=>6.40832

=>6.41 years.......(rounded to two decimals)