Question

You have been asked to estimate the appropriate discount rate to use in the evaluation of a new line of business. You have determined the market value of the firm’s target capital structure as follows:

Source of Capital	Market Value
Bonds	350,000
Preferred Stock	200,000
Common Stock	450,000

To finance the new project, the company will sell:

• 12-year bonds with a $1,000 par value paying 8% per year (paid semiannually) at the market price of $980.
• Preferred stock paying a $2.50 dividend and selling for $25.
• The firm’s common stock paid $3 dividend last year and expects dividends to continue growing at a rate of 6% per year indefinitely. The common stock is selling at $42 per share.

The firm’s marginal tax rate is 30%.

1. Estimate the discount rate that the firm needs to use to evaluate the project. (5 points)
2. In the analysis done so far we have not considered the effects of the floatation costs. Assume now that the company is raising a total of $1,000,000 using the above financing mix. New debt financing will require that the firm pays 100 basis points (i.e. 1%) in issue costs, the sale of preferred stock will require the firm to pay 250 basis points in flotation costs, and the common stock issue will require flotation costs of 500 basis points.
3. a. Estimate the total flotation costs the firm will incur to raise the needed $1 million. (2 points)

1. b. How should the flotation costs be incorporated into the analysis of the $1 million investment the firm plans to make? (1 point)

Answer 1

1. Discount rate the firm needs to use is its Weighted Average Cost of Capital, ie. WACC

We need to find the cost of its different sources of finance raised

Cost of bonds, kd

is the rate that equates the present values of its coupon & maturity value cashflows to its current markrtprice

ie. Equating $ 980 to the PV of its 12 yrs.*2=24 semi annual coupons +PV of Face value to be recd. At maturity

ie.980=((1000*8%/2)*(1-(1+r)^-24)/r)+(1000/(1+r)^24)

Solving for r, we get the semi-annual before-tax r as,

4.13297%

The annual before-tax r=

(1+4.13297%)^2-1=

0.084368

So, the after-tax r or yield on bonds=

After-tax cost =Before-tax cost*(1-Tax rate)

ie.0.084368*(1-30%)=

5.91%

Cost of Preferred stock, k ps= $ dividend/ Current market price

ie.2.50/25=

10.00%

Cost of Common stock,ke

as per gordon's dividend discount model

ke=(D1/P0)+g

where D1=the next dividend, ie. D0*(1+g), ie. 3.00*(1+0.06)=3.18

P0=the current market price , ie. $ 42/ share

g= growth rate of dividends = 6% p.a.

Now, plugging in the values in the formula,

ke=(3.18/42)+0.06=

13.57%

so, now the WACC=

(wt.d*kd)+(wt. ps*k ps)+(wt.e*ke)

ie.(35/100*5.91%)+(20/100*10%)+(45/100*13.57%)=

10.18%

2 a..Total Flotation cost, the firm will incur=(350000*1%)+(200000*2.5%)+(450000*5%)=

31000

2.b.Flotation cost will be treated as reduction in the net proceeds of the total amount collected by way of new issue.

In the given case, costs will be calculated as follows--with flotation costs on issue

Cost of bonds:

ie.980*(1-1%)=((1000*8%/2)*(1-(1+r)^-24)/r)+(1000/(1+r)^24)

Solving for r, we get the semi-annual before-tax r as,

4.19946%

The annual before-tax r=

(1+4.19946%)^2-1=

0.085753

So, the after-tax r or yield on bonds=

After-tax cost =Before-tax cost*(1-Tax rate)

ie.0.085753*(1-30%)=

6.00%

Cost of Preferred stock, k ps= $ dividend/ Current market price*(1-Flot. Cost%)

ie.2.50/(25*(1-2.5%))=

10.26%

Cost of Common stock,ke

as per gordon's dividend discount model

ke=(D1/P0)+g

where D1=the next dividend, ie. D0*(1+g), ie. 3.00*(1+0.06)=3.18

P0=net proceeds of current market price/share , ie. $ 42*(1-5%)=$ 39.9/ share

g= growth rate of dividends = 6% p.a.

Now, plugging in the values in the formula,

ke=(3.18/39.9)+0.06=

13.97%

so, now the WACC=

(wt.d*kd)+(wt. ps*k ps)+(wt.e*ke)

ie.(35/100*6%)+(20/100*10.26%)+(45/100*13.97%)=

10.44%