Question

If a project costs ​$70000 and is expected to return $16000 ​annually, how long does it take to recover the initial​ investment? What would be the discounted payback period at i=14​%?

Assume that the cash flows occur continuously throughout the year.

The payback period is ? years. ​(Round to one decimal​ place.) The discounted payback period at i=14​% would be ? years. What are the ?'s

Answer 1

Answer:

Given that:

if a Project costs $70000 and is expected to return $16000 annually.

Payback period:

Payback period = Initial investment / cash flow

Payback period = 70,000 / 16,000

Payback period = 4.3years

Discounted payback period:

Present value of year 1 cash flow = 16,000 / (1 + 0.14)1 = 14035.08

Present value of year 2 cash flow =16000 / (1 + 0.14)2 = 12500.00

Present value of year 3 cash flow = 16,000 / (1 + 0.14)3 = 11267.60

Present value of year 4 cash flow = 16,000 / (1 + 0.14)4 = 10256.41

Present value of year 5 cash flow = 16,000 / (1 + 0.14)5 = 9411.76

Present value of year 6 cash flow = 16,000 / (1 + 0.14)6 = 8695.65

Present value of year 7 cash flow = 16,000 / (1 + 0.14)7 = 8080.80

Cumulative cash flow for year 0 = -70,000

Cumulative cash flow for year 1 = -70,000 + 14035.08 = -55964.92

Cumulative cash flow for year 2 = -55964.92 + 12500 = -43464.92

Cumulative cash flow for year 3 = -43464.92 + 11,267.60 = -32197.32

Cumulative cash flow for year 4 = -32197.32 + 10256.41= -21940.91

Cumulative cash flow for year 5 = -21940.91 + 9411.76 = -12529.15

Cumulative cash flow for year 6 = -12529.15 + 8695.65 = -3833.5

Cumulative cash flow for year 7 = -3833.5 + 8080.80 = 4247.3

Discounted Payback Period at i = 14% would be = 6 + |-3833.5| / 8080.80 ≈ 6.47 years