Question

Consider two streams of cash flows, A and B. Stream A’s first cash flow is $9,800 and is received three years from today. Future cash flows in Stream A grow by 3 percent in perpetuity. Stream B’s first cash flow is −$9,100, is received two years from today, and will continue in perpetuity. Assume that the appropriate discount rate is 11 percent. a.What is the present value of each stream? b.Suppose that the two streams are combined into one project, called C. What is the IRR of Project C?

Answer 1

Given,

Stream A cashflow = $9800

Growth rate = 3%

Discount rate = 11%

Cashflows starts after 3years from today grows at 3% perpetuity

Computation of present value of stream A

Present value of casflows growing in perpetuity at the end of 3years from now = cashflow÷(discount rate - growth rate)

[9800]÷(11%-7%)= $122500

Present value of $122500 as on today will be $122500 ÷ (1.11×1.11×1.11)= $89570.9442

Therefore present value of streamA cashflows is $89570.9442

For Stream B

Cashflow = $(9100)

Cashflow will be received after 2years from now

Present value of cashflow at the end of 2nd year is $(9100)÷0.11 = $(82,727.2727)

Present value of cashflow as on today is $82,727.2727÷(1.11×1.11) = $(67143.3104)

Therefore present value under stream B is $(67,143.3104)

Computation of IRR

As given both are in same project one becomes inflow and other becomes outflow

Calculation of NPV at 23%

Stream A = $9800÷{[0.23- 0.03]×1.23×1.23×1.23} = $26,331.812

Stream B = $(9100)÷[0.23×1.23×1.23] = $(26,151.9052)

NPV = cashflows of stream A - cashflows of stream B = $161.9068

Calculation of NPV at 24%

Stream A = $9800÷{[0.24-0.03]×1.24×1.24} = $24476.0722

Stream B = $(9100)÷[0.24×1.24×1.24] = $(24,657.6427)

NPV = cashflows of stream A - cashflows of stream B = $(183.5705)

IRR of the project C =

lower rate + {[NPV at lowwr rate ÷ (NPV at lower rate - NPV at higher rate)]×difference in rate}

23% + [(161.9068)÷{161.9068-(-183.5705)}]×1 = 23.4686%

Therefore IRR of project C = 23.4686%