Question

Beckinridge Plastic Co plans to undertake one of the following two projects, say A and B, for this fiscal year. The cost of project A is $ 120,000 and the cost of B is also $120,000. The firm’s cost of capital is 7 % per year. After-tax cash flows are estimated to be $ 9,000 per year for 30 years for project A. After-tax cash flows for project B are expected to be $ 8,700 per year forever.

(a) Capital budgeting techniques are very sensitive to the choice of the cost of capital. At what interest rate would Beckinridge be indifferent between these two projects? That is, what is the interest rate at which NPVA = NPVB ? You must show your work and provide exact answer. Also, at this interest rate, what is the NPVA (or NPVB)? Please be precise.

Answer 1

Since investment is equal we need to find the rate at which present value of cash inflows are equal to achieve required cross over rate.

A is an annuity and B is perpetuity.

Present value of A cash inflows = Present value of B cash inflows

$9,000 × PVAF(r, 30) = $8,700/r

PVAF(r, 30) × r = 8700/9000 = 0.9666667

Below is an illustration of possible PVAF(r, 30) × r values at different interest rates:

r	Annuity factor 30 years for r	r × annuity factor
1%	25.8077	0.2580771
2%	22.3965	0.4479291
3%	19.6004	0.5880132
4%	17.2920	0.6916813
5%	15.3725	0.7686226
6%	13.7648	0.8258899
7%	12.4090	0.8686329
8%	11.2578	0.9006227
9%	10.2737	0.9246289
10%	9.4269	0.9426914
11%	8.6938	0.9563172
12%	8.0552	0.9666221

At 12% PVAF(r, 30) × r is equal to calculated amount of 0.9666

Cross over rate is 12%. It is the rate at which NPV of both projects are equal.

b

NPV of A = $9,000 × 8.0552 - $120,000 = -$47,503

NPV of B = $8,700/12% - $120,000 = - $47,500

Please rate.