Question

You are an original owner of a publicly traded food service company named Smith’s Foods (SF). Your company has been in the high-end restaurant business (HE) for the past ten years. You announced today that the company will be issuing debt today to open a new fast food division (FF). Opening this new division costs $10M today, which you will fund by issuing debt. Revenues from this new division are expected to be $3.5M next year and are projected to grow by 4 percent per year. Costs from this new division are expected to be $2M next year and are projected to grow by 2 percent per year. The life of this project is 15 years. Analyses of other fast food businesses suggest that the beta of a typical fast food division equals 0.70. Assume that the revenues and costs have similar risk. Throughout this problem, assume a risk-free rate of 3 percent and a market risk premium of 6 percent. a) What is the NPV of this new investment? Is the investment worthwhile? (Hint: you will need to use the growing annuity formula twice: once for revenues and once for costs.) A regression of monthly SF excess stock returns on monthly S&P 500 excess returns from the past ten years tells you that the beta of the high-end division equals 1.5. Directly before the investment in the fast food division, SF was an all-equity firm with 1M shares outstanding trading at $25 per share. This represents the value of the high-end division. Assume that the announcement of the new division does not affect the value or beta of the high-end division. b) What is the beta of the firm after the announcement of the new division? The beta of a firm can be calculated as the value-weighted average of the division betas: ?????????? = ????1 ????1 + ????2 ????1 + ????2 ????1 + ????2 ????2 where the value of the new division equals the present value of its future net cash flows (when calculating the value of the fast food division, do not subtract the initial $10M cost, as this was paid for using newly-issued debt). c) Assume that the beta of the new debt (valued at $10M) equals 0.1. What is the beta of the firm’s equity after the announcement of the new division? d) The beta of your firm’s equity was originally 1.5. There are two reasons why the announcement caused the beta of your firm’s equity to slightly change – one reason caused the original beta to decrease while the other caused it to increase. Briefly explain these reasons.

Answer 1

	In Millions
Outflow now	10
New division cost	2
cost growth	2%
Revenue	3.5
Revenue growth	4%
Life	15 Yrs
Discounting rate	RF+maket premium*Beta
	7.20%

Year	Inflow	Outflow	Net	Disc rate	PV
1	3.50	2.00	1.50	0.93	1.40
2	3.64	2.04	1.60	0.87	1.39
3	3.79	2.08	1.70	0.81	1.38
4	3.94	2.12	1.81	0.76	1.37
5	4.09	2.16	1.93	0.71	1.36
6	4.26	2.21	2.05	0.66	1.35
7	4.43	2.25	2.18	0.61	1.34
8	4.61	2.30	2.31	0.57	1.32
9	4.79	2.34	2.45	0.53	1.31
10	4.98	2.39	2.59	0.50	1.29
11	5.18	2.44	2.74	0.47	1.28
12	5.39	2.49	2.90	0.43	1.26
13	5.60	2.54	3.07	0.41	1.24
14	5.83	2.59	3.24	0.38	1.22
15	6.06	2.64	3.42	0.35	1.21
				Total Net Inflows	19.74
				Outflows	10.00
				NPV	9.74

*Inflow =3.5+(3.5*4%)=3.64. Similarly other inflow working is done

Outflows =2+(2*2%)=2.04  Similarly other outflow working is done.

Net is consider because you have inflow and outflow in same period.

Since NPV is positive Investment to be done since it would increase the value of the company.

Part B
	In Millions
	Value	Wtg	Beta
Value of High end Division =No. of shares * market rate	25.00	0.56	1.5
New Division value	19.74	0.44	0
	44.74	1.00
Firm Beta =Wtg HE *Beta of HE + Wtg of new *Beta of new division	0.84

Part C	In Millions
	Value	Wtg	Beta
Value of High end Division =No. of shares * market rate	25	0.56	1.5
New Division value	19.74	0.44	0.1
Firm Beta =Wtg HE *Beta of HE + Wtg of new *Beta of new division	0.88

Part D

The Beta of the company changed because now at present the company is levered(Debt issued ) after new division. Since the debt beta is lower than 1 it helps to reduce the overall beta of the company.