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a stream of cash flows that pays 100 every year for 10 years. the first cash...

a stream of cash flows that pays 100 every year for 10 years. the first cash flow is received at t=3. what is the Pv at time zero? what is the fav at time 12?


no discount rate

10% rate

Solutions

Expert Solution

The formula to calculate present value of cash flows = (Cash flow at year n)/ (1 + discount rate)n

Hence, the present value of the above stream of cash flows if discount is 10% is

$100/ (1+0.10)3 + $100/ (1+0.10)4 + $100/ (1+0.10)5 + $100/ (1+0.10)6 + $100/ (1+0.10)7 + $100/ (1+0.10)8 + $100/ (1+0.10)9 + $100/ (1+0.10)10 +$100/ (1+0.10)11 + $100/ (1+0.10)12

= $75.13 + $68.30 + $62.09 + $56.44 + $51.32 + $46.65 + $42.41 + $38.55 + $35.05 + $31.86 = $507.81

The present value of the above stream of cash flows if there is no discount rate or 0%

= $100/ (1+0)3 + $100/ (1+0)4 + $100/ (1+0)5 + $100/ (1+0)6 + $100/ (1+0)7 + $100/ (1+0)8 + $100/ (1+0)9 + $100/ (1+0)10 +$100/ (1+0)11 + $100/ (1+0)12

= $100/ 1 + $100/ 1 + $100/ 1 + $100/ 1 +$100/ 1 + $100/ 1 + $100/ 1+ $100/ 1 + $100/ 1 + $100/ 1 = $1,000

Now we need to find the future value of these cash flows at year 12.

The formula is (Cash flow at year n) * (1 + discount rate)(12-n)

Hence, the future value at year 12, if discount rate is 10%

= $100* (1+0.10)12-3 + $100/ (1+0.10)12-4 + $100/ (1+0.10)12-5 + $100/ (1+0.10)12-6 + $100/ (1+0.10)12-7 + $100/ (1+0.10)12-8 + $100/ (1+0.10)12-9 + $100/ (1+0.10)12-10 +$100/ (1+0.10)12-11 + $100/ (1+0.10)12-12

= $100* (1+0.10)9 + $100* (1+0.10)8 + $100* (1+0.10)7 + $100* (1+0.10)6 + $100 *(1+0.10)5 + $100* (1+0.10)4 + $100* (1+0.10)3 + $100* (1+0.10)2 +$100* (1+0.10)1 + $100* (1+0.10)0

= $235.79 + $214.36 + $194.87 + $177.15 + $161.05 + $146.41 + $133.1 + $121 + $110 + 100 = $1,593.74

the future value at year 12, if discount rate is 0% is

$100* (1+0.00)9 + $100* (1+0.00)8 + $100* (1+0.00)7 + $100* (1+0.00)6 + $100 *(1+0.00)5 + $100* (1+0.00)4 + $100* (1+0.00)3 + $100* (1+0.00)2 +$100* (1+0.00)1 + $100* (1+0.00)0

$100* 1 + $100* 1 + $100* 1 + $100*1 +$100* 1 + $100* 1 + $100* 1+ $100* 1 + $100* 1 + $100*1 = $1,000

jeff jeffy answered 6 months ago
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