Question

A start-up internet service provider expects to gain money in each of the first four years. Gains are projected to be $50 million in year one, $60 million in year two, $70 million in year three and $100 million in year four. An interest rate of 10% per year is used.
A. Draw the cash flow diagram.
B. What is the present worth of the gains for the first three years?
C. What is the present worth of the gains for all four years?
D. What is the equivalent uniform annual worth of the gains through year four?

Answer 1

Answer:

A. Draw the cash flow diagram.

since the site doesn't include a drawing tool I just prepared a table to depict cash flows associated to years one through four:

Year                   Cash inflows

1                            $50 million        

2                           $60 million  

3                           $70 million  

4                           $100 million  

B. What is the present worth of the gains for the first three years?

• the present value of the first three cash flows = $50/1.1 + $60/1.1² + $70/1.1³ = $45.45 + $49.59 + $52.59 = $147.63 million

C. What is the present worth of the gains for all four years?

• the present value of the first three cash flows = $50/1.1 + $60/1.1² + $70/1.1³ + $100/1.1⁴ = $45.45 + $49.59 + $52.59 + $68.30 = $215.93 million

D. What is the equivalent uniform annual worth of the gains through year four?

• equivalent annual worth = (NPV x r) / [1 - (1 + r)⁻ⁿ] = ($215.93 x 0.1) / [1 - (1 + 0.1)⁻⁴] = 21.593 / 0.31699 = $68.12 million