Question

An investment project has annual cash inflows of $4,000, $4,900, $6,100, and $5,300, for the next four years, respectively. The discount rate is 13 percent.What is the discounted payback period for these cash flows if the initial cost is $6,700?What is the discounted payback period for these cash flows if the initial cost is $8,800?What is the discounted payback period for these cash flows if the initial cost is $11,800?

Answer 1

Answer:

(A) Investment of  6,700 discount payback period  1.82

(B) Investment of  8,800 discount payback period 2.34

(C) Investment of 11,800 discount payback period 3.06

Explanation:

We will discount each cash flow at 13%

$\frac{4,000}{(1 + 0.13)^{1} } = PV$

3539.823

$\frac{4,900}{(1 + 0.13)^{2} } = PV$

3837.4187

$\frac{6,100}{(1 + 0.13)^{3} } = PV$

4227.606

$\frac{5,300}{(1 + 0.13)^{4} } = PV$

3250.5893

We need to look at which year we get the investment amount

We will do: accumalted cash flow less investment

and then divide by the last year to get at which portion of this year we achieve payback period

(A) 6,700

3540 + 3837 = 7377

It will be between the first and second year

6,700 - 3,540 = 3160

3160/3837 = 0.8235

payback period  1.8235

(B) 8,800

3540 + 3837 + 4228 = 11605

It will be between second and third year

we do 8,800 - 7377 = 1423

1423/4228 = 0.3365

payback 2.3365

(C) 11,800

3540 + 3837 + 4228 + 3251 = 14856

It will be between third and fourth year

11,800-11,605 = 195

195/3251 = 0.0599 = 0.06

payback 3.06