Question

PROBLEM 13-30 Internal Rate of Return: Sensitivity Analysis [L02] In my opinion, a tanning salon would be a natural addition to our spa and very popular with our customers. said Stacey Winder, manager of the Lifeline Spa. "Our figures show that we could remodel the building next door to our spa and install all of the necessary equipment for $330,000. I have contacted tanning salons in other areas, and I am told that the tanning beds will be usable for about nine years. I am also told that a four-bed salon such as we are planning would generate a cash inflow of about $80,000 per year after all expenses "It does sound very appealing." replied Kevin Leblanc, the spa's accountant. "Let me push the num bers around a bit and see what kind of a return the salon would generate." 1. 2. Compute the intermal rate of return promised by the tanning salon to the nearest whole percent. Assume that Ms. Winder will not open the salon unless it promises a return of at least 14%. Compute the amount of annual cash inflow that would provide this return on the $330,000 investment. Although nine years is the average life of tanning salon equipment, Ms. Winder has found that this life can vary substantially. Compute the internal rate of return to the nearest whole percent if the life were (a) 6 years and (b) 12 years rather than 9 years. Is there any information provided by these computations that you would be particularly anxious to show Ms. Winder? Ms. Winder has also found that although $80,000 is an average cash inflow from a four-bed salon, some salons vary as much as 20% from this figure. Compute the internal rate of return to the nearest whole percent if the annual cash inflows were (a) 20% less and (b) 20% greater than S80.000. 3. 4. 5. Assume that the $330,000 investment is made and that the salon is opened as planned. Because of concerns about the effects of excessive tanning, however, the salon is not able to attract as many cus tomers as planned. Cash inflows are only $50,000 per year, and after eight years the salon equipment is sold to a competitor for $135,440. Compute the internal rate of return to the nearest whole percent camed on the investment over the eight-year period. (Hint: A useful way to proceed is to find the dis count rate that will cause the net present value to be equal to, or near, zero.)

Answer 1

Answer 1:

Using IRR function of excel we find (please see calculations as below):

IRR = 19%

Answer 2:

Annual cash flow required to result in 14% return on $330,000

The discounted cash flows when discounted at 14% should be at least = $330,000

PV Factors for a One-Dollar Annuity Discounted at 14% for 9 Periods = [1 - 1/(1 + k) ⁿ] / k

= (1 - 1/(1+14%) ⁹ ) /14%

= 4.9463718

Hence:

Annual cash flow required =  Discounted cash flow / PV factor = $330,000 / 4.9463718 = $66,715.57

Annual cash flow = $66,715.57

Answer 3:

(a) IRR = 12%

(B) IRR = 22%

Answer 4:

(a) IRR = 13%

(B) IRR = 25%

Answer 5:

IRR = 10%