Question

Consider a project of the Pearson Company (as in an example from Lecture 3 slides). The timing and size of the incremental after-tax cash flows for an equity-financed project are:

Year	0	1	2	3	4
CF	-1,000	325	250	375	500

The firm is financing the project with $600 debt which carries 8% interest rate. The firm currently has no leverage, faces 40% tax rate and has 10% cost of capital. Value the project using flow to Equity Valuation

Answer 1

Valuation of Equity

FLOW TO EQUITY

Step 1

Outflow=$1000

Debt=$600

Equity=$400(1000-600)

Interest payment=$600*0.08%=$48

Tax saving on Interest=$19.2 (48*40%)

Interest after tax saving =$48-$19.2=$28.8

Step2

Lets analyze Cash flow Position of equity holders

Cash INFLOW -interest after tax for the year 1-4

And in the last year payment of $600 debt principal to be made.

Therefore cash flow table FREE CASH FLOW TO EQUITYHOLDERS

Year	Cash Flow
0	-$400
1	$325-$28.8=$296.2
2	$250-$28.8=$221.2
3	$375-$28.8=$346.2
4	$500-28.8-600=$-128

Step 3

Using the above formula we can calculate cost of levered equity capital=

Lets understand the formula

Ru=Unlevered cost of capital given in the question 10%

Rb=cost of debt=8%

T= tax rate 40%

B=value of debt=$600

E=market value of equity=?

Hence we have to find E

(It can be assumed to be Initial investment =$400) alternatively to arrive at more precise value will be discounting the cash flows and tax saving from debt financing

=

1188.91-600=$588.91

Hence now we can calculate Re (as written above even 400 can be taken but for a precise value i have taken 588.91 the discounted value)

=(

Therefore NPV

Cash INFLOW-cash iOUTFLOW

Cash Outflow=$400

Cash inflow as given for 1-4 years will be discounted at 11.22%

612.6-400=$212.60

Hence NET PRESENT VALUE =$212.60.