Discounted payback: Carmen Electronics bought new machinery for $5 million. This is expected to result in additional cash flows of $1.2 million over the next seven years. The firm's cost of capital is 12 percent. What is the discounted payback period for this project? If the firm's acceptance period is five years, will this project be accepted?

Question

Quizplus · Accepted Answer

To calculate the discounted payback period, we need to calculate the present value of the cash flows and accumulate them until we recover the initial investment of $5 million.

Year 1: $1.2 million/ (1+0.12)^1 = $1.07 million
Year 2: $1.2 million/ (1+0.12)^2 = $0.95 million
Year 3: $1.2 million/ (1+0.12)^3 = $0.84 million
Year 4: $1.2 million/ (1+0.12)^4 = $0.75 million
Year 5: $1.2 million/ (1+0.12)^5 = $0.67 million
Year 6: $1.2 million/ (1+0.12)^6 = $0.60 million
Year 7: $1.2 million/ (1+0.12)^7 = $0.54 million

Accumulated cash flows:
Year 1: $1.07 million
Year 2: $2.02 million
Year 3: $2.86 million
Year 4: $3.61 million
Year 5: $4.28 million
Year 6: $4.88 million
Year 7: $5.42 million

The discounted payback period is between 5 and 6 years, when we recover the $5 million initial investment. Therefore, the answer is B.

Since the project does not recover the initial investment within the acceptance period of five years, it will not be accepted.

Discounted Payback: Carmen Electronics Bought New Machinery for $5 Million