Question

3. Consider Table 2 Table 2 Year 3 Year 4 Cash flow Year 2 Year 0 Year 1 Cash flovw Cash flow Cash flow 70 Cash flow Project 80 70 30 -150 0.24 Interest Tax Shield 0.75 (a)Consider Table 2. Calculate the net present value of the project assuming it is all-equity financed. The required return on unlevered equity is 15%. (b)Consider Table 2. Assume for now that the project is financed using equal parts debt and equity. The cost of debt capital is 10%. Calculate the required return on levered equity and the (after-tax) weighted average cost of capital (WACC) (c)Consider Table 2. Assume for now that the project is financed using equal parts debt and equity. Using the (after-tax) weighted average cost of capital (WACC) approach, calculate the net present value of the levered project. (d)Consider Table 2. Assume for now that the project is financed using equal parts debt and equity. Calculate the adjusted present value (APV) of the levered project.

Answer 1

Answer a)

NPV of a project = Present value of cash inflow – Initial investment cost

Calculation of present value of cash inflow where cost of capital is given 15%

$80 ˣPV(15%,1y) + $70 ˣPV(15%,2y) + $70 ˣPV(15%,3y) + $30 ˣPV(15%,4y)

= $80 ˣ .870 + $70 ˣ.756 + $70 ˣ.658 + $30 ˣ.572

= $69.6 + $52.92 + $46.06 + $17.16

=$185.74

Initial investment cost = $150 which is made entirely through equity

NPV of a project = Present value of cash inflow – Initial investment cost

                   NPV = $185.74 - $150

                            = $35.74

Answer b)

Determination of cost of equity when investment ratio between equity and debt is 1:1

If we consider determination of cost of equity before taxes

As per MM theorem the formula of cost of equity is

Cost of equity = Cost of unlevered equity + Debt / Equity (cost of Unlevered equity – cost of debt)

= 15% + .75/.75 (15% - 10%)

= 15% - 5%

= 10%

Therefore, cost of equity = 10% when debt capital is introduced at 1:1 ratio

Calculation of WACC

Calculation of weighted average cost of capital
								WACC
Year	Item	Amount	Weight	Pre tax cost	Tax sheild	Post tax cost	Weighted cost(WACC)	Percentage(%)
1	Equity	75	0.5	7.5	N.A.	7.5	3.75
	Debt	75	0.5	7.5	3	4.5	2.25
						Total cost	6	4
Year 2	Equity	75	0.5	7.5		7.5	3.75
	Debt	75	0.5	7.5	2	5.5	2.75
						Total cost	6.5	4.33
Year 3	Equity	75	0.5	7.5		7.5	3.75
	Debt	75	0.5	7.5	0.75	6.75	3.375
						Total cost	7.125	4.75
Year 4	Equity	75	0.5	7.5		7.5	3.75
	Debt	75	0.5	7.5	0.24	7.26	3.63
						Total Cost	7.38	4.92

Answer 3

Calculation of net present value of the project by using WACC rate

NPV = $80 ˣPV(4%,1y) + $70 ˣPV(4.33%,2y) + $70 ˣPV(4.75%,3y) + $30 ˣPV(4.92%,4y) – Initial capital

=    14+13.13 +12.18+5.06 - $150

=$44.37 - $150

NPV = ($105.63)

Answer d)

Solely financed by equity capital + present value of financing

= $75 + $80 ˣPV(10%,1y) + $70 ˣPV(10%,2y) + $70 ˣPV(10%,3y) + $30 ˣPV(10%,4y)

= Total value of this summation is APV