Question

Ginny Trueblood is considering an investment which will cost her $120,000. The investment produces no cash flows for the first year. In the second year the cash inflow is $35,000. This inflow will increase to $55,000 and then $75,000 for the following two years before ceasing permanently. Ginny requires a 10% rate of return and has a required discounted payback period of three years. Ginny should this project because the discounted payback period is___________ . A.accept; 2.03 years B.accept; 2.97 years C.accept; 3.97 years D.reject; 3.03 years E.reject; 3.97 years

Answer 1

The project should be rejected as the payback period of 3.97 years exceeds the required 3 years. So, the correct option is E

Step-by-step explanation:

The table showing the discounted cash flows of each year:

Computing discounted payback as:

Discounted Payback = Number of years + (Initial Cost - Discounted Cash flow of year 1 + Discounted Cash flow of year 2 + Discounted Cash flow of year 3 / Discounted Cash flow of year 4)

= 3 + ($120,000 - $0 - $28,925.62 - $41,322.31 / $51,226.01)

= 3 + ($49,752.07 / $51,226.01)

= 3 + 0.97

= 3.97

Working Note:

Discounted Cash Flow is computed as:

Discounted cash flow = Cash Flow / (1 + r) ^ n

where

r is rate of return that is 10%

n is number of year

So,

For 1st year:

= $0 / (1 + 0.1) ^1

= $0

For 2nd year:

= $35,000 / (1 + 0.1) ^ 2

= $35,000 / 1.21

= $28,925.61

For 3rd year:

= $55,000 / (1 + 0.1) ^ 3

= $55,000 / 1.331

= $41,322.31

For 4th year:

= $75,000 / (1 + 0.1) ^ 4

= $75,000 / 1.4641

= $51,226.01