Question

The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $56 million on a large-scale, integrated plant that will provide an expected cash flow stream of $9 million per year for 20 years. Plan B calls for the expenditure of $12 million to build a somewhat less efficient, more labor-intensive plant that has an expected cash flow stream of $3.8 million per year for 20 years. The firm's cost of capital is 11%.
Calculate each project's NPV. Round your answers to the nearest dollar.

Calculate each project's IRR. Round your answers to two decimal places.

Set up a Project
Δ
by showing the cash flows that will exist if the firm goes with the large plant rather than the smaller plant.

Year 0

Years 1-20

What is the NPV for this Project
Δ
? Round your answer to the nearest dollar.

What is the IRR for this Project
Δ
? Round your answer to two decimal places.

Answer 1

Answer:

NPV of Plan A: $15,669,953.

NPV of Plan B: $18.260,647.

For the Plan A, the IRR is r=0.15.

For the Plan B, the IRR is r=0.32.

Explanation:

We have two expansion plans:

Plan A:

- Expenditure: -$56 million

- Cash flow: $9 million/year

- Duration: 20 years

Plan B:

- Expenditure: -$12 million

- Cash flow: $3.8 million/year

- Duration: 20 years

The NPV of plan A can be expressed as:

$NPV_A=-I_0+\sum_{k=1}^{20} (CF_k)(1+i)^{-k}\\\\NPV_A=-I_0+(CF)[\frac{1-(1+i)^{-20}}{i}] \\\\NPV_A=-56+9*[\frac{1-(1.11)^{-20}}{0.11}]=-56+9*\frac{0.876}{0.11}=-56+9*7.963328117 \\\\NPV_A=-56+71.66995306= 15.669953$

NPV of Plan A: $15,669,953.

The NPV of plan B can be expressed as:

$NPV_B=-I_0+\sum_{k=1}^{20} (CF_k)(1+i)^{-k}\\\\NPV_B=-I_0+(CF)[\frac{1-(1+i)^{-20}}{i}] \\\\NPV_B=-12+3.8*[\frac{1-(1.11)^{-20}}{0.11}]=-12+3.8*\frac{0.876}{0.11}=-12+3.8*7.963328117\\\\NPV_B=-12+30.26064685=18.260647$

NPV of Plan B: $18.260,647.

To calculate the IRR, we have to clear the discount rate for NPV=0. We can not solve this analitically, but we can do it by iteration (guessing) or by graphing different NPV, with the discount rate as the independent variable.

For the Plan A, the IRR is r=0.15.

For the Plan B, the IRR is r=0.32.