Question

The conventional payback period ignores the time value of money, and this concerns Green Caterpillar's CFO. He hwas now asked you to compute Alpha's discounted payback period, assuming the company has a 10% cost of capital.
Year 0 Year 1 Year 2 Year 3
Cash flow -5,000,000 2,000,000 4,250,000 1,750,000
Discounted cash flow ? ? ? ?
Cumulated discounted cash flow ? ? ? ?
Discounted payback period ?

Required:
How much value in this example does the discounted payback period method fail to recognize due to this theoretical deficiency?

Answer 1

Answer: $‭1,645,379.41‬

Explanation:

The deficiency attached to the Discounted Payback period is that it stops recognizing cashflows after the project is paid off.

Year 1 discounted cash flow = 2,000,000/(1 + 10%) = $1,818,181.82

Year 2 discounted cashflow = 4,250,000 / (1 + 10%)² = $3,512,396.69

Year 3 discounted cashflow = 1,750,000/( 1 + 10%)³ = $1,314,800.90

Amount that Discounted Payback period will not recognize is;

= Cumulated discounted cash flow - Initial cost

= 1,818,181.82 + 3,512,396.69 + 1,314,800.90 - 5,000,000

= $‭1,645,379.41‬