Question

The Yurdone Corporation wants to set up a private cemetery business. According to the CFO, Barry M. Deep, business is "looking up." As a result, the cemetery project will provide a net cash inflow of $98,000 for the firm during the first year, and the cash flows are projected to grow at a rate of 3 percent per year forever. The project requires an initial investment of $1,510,000.

  

a-1

What is the NPV for the project if the company's required return is 12 percent? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV = ________ a-2 If the company requires a return of 12 percent on such undertakings, should the cemetery business be started? No Yes    b. The company is somewhat unsure about the assumption of a growth rate of 3 percent in its cash flows. At what constant growth rate would the company just break even if it still required a return of 12 percent on investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Constant Growth Rate = _________ %

Answer 1

Year 0 - intitial investment of $1,510,000

Year 1 - $98,000

Year 2 - 98,000*(1+g) -----where g is the growth rate of 3%

Year 3 - 98,000*(1+g)*(1+g).....so on and so forth.

To calculate the Present value of all the net cash flows from Year 1 to infinity, we have to use the formula = Year 1 Cash Flow/(r-g) --->where r is the discount rate given, which is 12% and g is the growth rate of 3%

Note : This formula is the Sum of terminating infinite series Geometric Progression. A geometric such as 2,1,1/2,...is a terminating infinite series Geometric Progression and has a finite sum which is given by the formula :- first term/(1 - common ratio). In the above Geometric progression, the common ratio is 1/2 (since the next term is always half of the initial term). With a little bit of algrebra, you can derive the Present Value = Year 1 cash flow/(Discount rate - growth rate

By plugging in values of r and g, we obtain the Present value of the Cash flows from year 1 to year infinity = 98,000/(0.12-0.03) = $1,088,888.89.

To calculate the NPV of the investment, we have to use the formula,

NPV = -initial investment + Present Value of all the cash flows over the life of the investment

= -1,510,000+ 1,088,888.89

= -421,111.11

Answer for part a) No. Because when we use a discount rate of 12%, we get a negative NPV. You should never accept projects which have negative NPV values. Therefore the cemetery business should not be started.

Answer for part b)

The company is unsure about the growth rate. So, basically we have to calculate the growth rate "g" at which there will be breakeven

Recall from the above NPV formula that

NPV = -initial investment + Present Value of all the cash flows over the life of the investment

= -1,510,000 + () -----as determined by the formula above

At Break Even, NPV = 0.

So,

0 = -1,510,000 + ()

1,510,000 =

(0.12 - g) = 98,000/1,510,000

= 0.06490

So, g = 0.551 or 5.51%