Which cash flow below has the largest present value if the interest rate is 8% p

Question

Which cash flow below has the largest present value if the interest rate is 8% per year? (Assume that the cash flows are received at the end of each year.)

A. A                B. B                C. C

          Year                    A                   B                        C                  

1                      $400                $400                $1,000

2                      $400                $0                    $50     

3                      $400                $0                    $50

4                      $0                    $0                    $0

5                      $0                    $900                $0

Explanation / Answer

Interest rate, r: 8%

A: Year 1: $400, Year 2: $400, Year 3: $400, Year 4: $0, Year 5: $0

Present Value of cash flows of A: Future Value / (1+r)^n where n = 1,2,3,4,5

= (400/(1+8%))+(400/(1+8%)^2)+(400/(1+8%)^3)+(0/(1+8%)^4)+(0/(1+8%)^5)

A = $1,030.84

B: Year 1: $400, Year 2: $0, Year 3: $0, Year 4: $0, Year 5: $900

Present Value of cash flows of B: Future Value / (1+r)^n where n = 1,2,3,4,5

= (400/(1+8%))+(0/(1+8%)^2)+(0/(1+8%)^3)+(0/(1+8%)^4)+(900/(1+8%)^5)

B = $982.90

C: Year 1: $1000, Year 2: $50, Year 3: $50, Year 4: $0, Year 5: $0

Present Value of cash flows of C: Future Value / (1+r)^n where n = 1,2,3,4,5

= (1000/(1+8%))+(50/(1+8%)^2)+(50/(1+8%)^3)+(0/(1+8%)^4)+(0/(1+8%)^5)

C  = $1,008.48

Based on the above calculations, Present Value of Cash Flow of A is the largest.

Hence, the answer is option A

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