Question

Consider Table 2 3. Table 2 CF3 CF4 CF2 CF1 CFO Project 75 40 60 110 110 (200) (200) (200) 75 40 60 75 40 60 110 0.80 0.24 2.00 3.60 Interest Tax Shield Additional information for all projects 15% Cost (required return) on unlevered equity (%) Cost of debt capital (%) Corporation tax rate (%) Financing of each project: Debt 10% 20% 100 100 Equit alculate the value of project 1 assuming that the project is entirely equity-financed w financed using equal parts debt and equity (100 of each). Calculate the r when debt finance is used (b) Consider Table 2. Project 1 is no adjusted present value (APV) of project 1. Why is the value of Project 1 greate to part-finance the project? (c) Consider Table 2. Consider Project 2 w the required return on levered equity and the (after-tax) weighted average cost of c Calculate the value of levered Project 2 using the after-tax WACC method. (d) Consider Table 2. Consider Project 3. Further assume that the fir project. Calculate the value of Project 3 using the after-tax WACC method ced using equal parts debt and equity. Calculate apital (WACC) hich is also finan uses debt only i.e. 200, to finance the

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Answer 1

a). Value of project 1 =  $\sum (CF_{t})/(1+rsU)^{t}$

where CFt = cash flow at time t and rsU = cost of unlevered equity = 15%

Vu = -200 + 110/(1+15%)^1 + 60/(1+15%)^2 + 75/(1+15%)^3 + 40/(1+15%)^4

= -200 + 95.65 + 45.37 + 49.31 + 22.87 = 13.20

b). If project 1 is equally financed by debt and equity then using APV approach

Value of levered project 1 VL = Vu + Present value (PV) of interest tax shield (discounted at rsU)

PV of interest tax shield = 3.60/(1+15%)^1 + 2/(1+15%)^2 + 0.80/(1+15%)^3 + 0.24/(1+15%)^4

= 3.13 + 1.51 + 0.53 + 0.14 = 5.31

VL = 13.20 + 5.31 = 18.51

Value of levered project is greater than the value of unlevered project because of the interest tax shield. This is why, debt financing (in part) is preferred because it lowers cost of capital and increases value.

c). Cost of levered equity rsL = rsU + (rsU - rd)*(D/E)*(1-Tax rate)

where rd = cost of debt = 10% and D/E (debt/equity) = 100/100 = 1

rsL = 15% + (15%-10%)*1*(1-20%) = 19%

Since D/E = 1, therefore D/(D+E) = 1/(1+1) = 1/2 and E/(D+E) = 1-1/2 = 1/2

After-tax WACC = D/(D+E)*rd*(1-Tax rate) + E/(D+E)*rsL

= 1/2*10%*(1-20%) + 1/2*19% = 13.5%

Value of levered project 2 =  

(CFt Interestshield)/(1 WACC)

= -200 + (110+/(1+13.5%)^1 + (60+2)/(1+13.5%)^2 + (75+0.80)/(1+13.5%)^3 + (40+0.24)/(1+13.5%)^4

= -200 + 98.78 + 46.88 + 49.84 + 23.01 = 18.51 (same as that calculated in part b)

d). After-tax WACC = D/(D+E)*rd*(1-Tax rate) = 1*10%*(1-20%) = 8%

Value of 100% debt financed project 3 =  

(CFt Interestshield)/(1 WACC)

= -200 + (110+/(1+8%)^1 + (60+2)/(1+8%)^2 + (75+0.80)/(1+8%)^3 + (40+0.24)/(1+8%)^4

= - 200 105.19 + 53.16 + 60.17 + 29.58 = 48.09