Question

PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM

An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $350 at the end of Year 5, and $550 at the end of Year 6.

1. If other investments of equal risk earn 4% annually, what is its present value? Round your answer to the nearest cent.

   $  

2. If other investments of equal risk earn 4% annually, what is its future value? Round your answer to the nearest cent.

   $  

Answer 1

Given,

Cash flow for first three years = $50

Year 4 cash flow = $250

Year 5 cash flow = $350

Year 6 cash flow = $550

Interest rate (r) = 4% or 0.04

Solution :-

(a)

Present value

= [cash flow for first three years/r x {1 - (1 + r)^-3}] + [year 4 cash flow x (1 + r)^-4] + [year 5 cash flow x (1 + r)^-5] + [year 6 cash flow x (1 + r)^-6]

= [$50/0.04 x {1 - (1 + 0.04)^-3}] + [$250 x (1 + 0.04)^-4] + [$350 x (1 + 0.04)^-5] + [$550 x (1 + 0.04)^-6]

= [$1250 x {1 - (1.04)^-3}] + [$250 x (1.04)^-4] + [$350 x (1.04)^-5] + [$550 x (1.04)^-6]

= [$1250 x {1 - 0.88899635867}] + [$250 x 0.854804191] + [$350 x 0.82192710675] + [$550 x 0.79031452573]

= [$1250 x 0.11100364133] + $213.70104775 + $287.674487362 + $434.672989151

= $138.754551662 + $213.70104775 + $287.674487362 + $434.672989151

= $1074.80307592 or $1074.80

(b)

Future value = present value x (1 + r)⁶

= $1074.80307592 x (1 + 0.04)⁶

= $1074.80307592 x (1.04)⁶

= $1074.80307592 x 1.26531901849 = $1359.97