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ou are given the following stream of cash flows: Year 1 Year 2 Year 3 Year...

ou are given the following stream of cash flows: Year 1 Year 2 Year 3 Year 4 Year 5 $100,000 $110,000 $120,000 $130,000 $140,000 A. If you thought the appropriate discount rate was 10%, what would be the present value of this cash flow stream today at t=0? B. If you thought the appropriate interest/discount rate was 10%, what would be the future value of this cash flow stream in five years at t=5 years?

Solutions

Expert Solution

Present Value calculation

Present Value is calculated using the below formula:

PV = Cn/(1+r)n

where r is the discount rate, Cn is the cash flow at year n

C1 = 100000, C2 = 110000, C3 = 120000, C4 = 130000, C5 = 140000

Present value of C1 = 100000/(1+10%)1 = 100000/(1.1)1 = 90909.0909090909

Present value of C2 = 100000/(1+10%)2 = 100000/(1.1)2 = 90909.0909090909

Present value of C3 = 100000/(1+10%)3 = 100000/(1.1)3 = 90157.7761081893

Present value of C4 = 100000/(1+10%)4 = 100000/(1.1)4​​​​​​​ = 88791.7491974592

Present value of C5 = 100000/(1+10%)5 = 100000/(1.1)5​​​​​​​ = 86928.9852282817

Total Present value = 447696.692352112

Year 1 2 3 4 5
Cash flow 100000 110000 120000 130000 140000
Present value 90909.09 90909.09 90157.78 88791.75 86928.99

Future value calculation

Future value is calculated using the below formula

FV = C*(1+r)n

Year 1 2 3 4 5
Cash flow 100000 110000 120000 130000 140000

Future value of C1 at (t=5) = 100000*(1+10%)4 = 100000*1.14 = 146410

Future value of C2 at (t=5) = 100000*(1+10%)3 = 100000*1.13 = 146410

Future value of C3 at (t=5) = 100000*(1+10%)2 = 100000*1.12 = 145200

Future value of C4 at t=5 = 100000*(1+10%)1 = 100000*1.11 = 143000

Future value of C5 at t=5 = 140000

Total future value at t=5) = 146410+146410+145200+143000+140000 = 721020

Year 1 2 3 4 5
Cash flow 100000 110000 120000 130000 140000
Future value 146410 146410 145200 143000 140000

jeff jeffy answered 3 months ago
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