Question

The Biological Insect Control Corporation (BICC) has hired you as a consultant to evaluate the NPV of its proposed toad ranch. BICC plans to breed toads and sell them as ecologically desirable insect control mechanisms. They anticipate that the business will continue into perpetuity. Following the negligible start-up costs, BICC expects the following nominal cash flows at the end of the year: Revenues $ 282,000 Labor costs 202,000 Other costs 72,000 The company will lease machinery for $107,000 per year. The lease payments start at the end of Year 1 and are expressed in nominal terms. Revenues will increase by 6 percent per year in real terms. Labor costs will increase by 5 percent per year in real terms. Other costs will increase by 3 percent per year in real terms. The rate of inflation is expected to be 8 percent per year. The required rate of return is 13 percent in real terms. The company has a 22 percent tax rate. All cash flows occur at year-end. What is the NPV of the proposed toad ranch today?

Answer 1

Solution:

The real value of each cash flow is the present value of the Year 1 nominal cash flows, discounted back at the present at the inflation rate. So, the real value of the revenue and costs will be:

Revenue in real terms = $282,000 / 1.08 = $261,111.11

Labour costs in real terms = $202,000 / 1.08 = $187,037.03

Other costs in real terms = $72,000 / 1.08 = $66,666.67

Lease payment of Machinery in real terms = $107,000 / 1.08 = $99,074.07

Revenue and all other costs are growing perpetuities, and having different growth rates, so we have to calculate present value for each separately using the real required return:

PV_Revenue       = $261,111.11 / (.13 − .06) = $3,730,158.71

PV_{Labour costs} = $187,037.03 / (.13 − .05) = $2,337,962.87

PV_{Other costs}     = $66,666.67/ (.13 − .03)   = $666,666.7

The lease payments are constant in nominal terms, therefore the lease payments having a growing perpetuity with negative growth rate, the present value of lease payments will be :

PV_{Lease Payments} = $99,074.07 / [.13 – (-.08)] = $471,781.28

NPV is the present value of the future after-tax cash flows. The NPV of the project is :

NPV = ( PV_Revenue - PV_{Labour costs} - PV_{Other costs} - PV_{Lease Payments})(1-tc)

NPV = ($3,730,158.71-$2,337,962.87-$666,666.7-$471,781.28)(1-.22)

NPV = ($253,747.86)(.78)

NPV = $197,923.33