Answer:
a. The cemetery business be started
b. The company will just break even at a constant growth rate of 4.4%
Explanation:
A. To know whether to start the cemetery business or not, we need to subtract the present value of the initial outlay to generate the NPV and if the result is positive, it will be advisable to start the business and if otherwise, it won't be advisable to start the cemetery business.
This is a question on perpetuity growth. let us extract the information in the question
Initial investment = $1,425,000
Cash inflow in year 1 (C) = $109,000
Cost of capital (r) = 12%
Growth Rate (g) = 5.1%
Net Present Value (NPV) = PV of Growing Perpetuity - Initial
investment
NPV = {C/(r-g)} - Initial Investment
NPV = {109,000 /(12% - 5.1%)} - 1,425,000
NPV = {109,000 /(0.12 - 0.5.1)} - 1,425,000
NPV = {109,000 /(0.69)} - 1,425,000
NPV = 1,579,710.15 - 1,425,000
NPV = $154,710.15
Since the net present value (NPV) of the project is positive, the cemetery business should be started.
b. At break even, PV of Growing Perpetuity = Initial investment
C/(r-g) = Initial investment
Initial investment = 1,425,000
C = $109,000
r = 12%
g = Unknown
109,000 /(12% - g) = 1,425,000
109,000 /(0.12 - g) = 1,425,000
1,425,000 (0.12 - g) = 109,000
171,000 - 1,425,000g = 109,000
- 1,425,000g = 109,000 - 171,000
- 1,425,000g = -62,000
- 1,425,000g/ - 1,425,000 = -62,000/- 1,425,000
g = 0.04351
Convert the answer to percentage 0.04351 * 100% = 4.4%
That is, the company will just break even at a constant growth rate of 4.4%
[ where a is a constant]