# Calculating NPV to equity holders problem

Hi, so I’m working on problem sets with solutions. However, the solutions does not include the calculations, only the correct answers. I’ve done most of them, but a couple of them are driving me absolutely nuts. Like this one:

Ciao Inc. wants to raise \$26 million in equity for a new project. In addition Ciao is planning to undertake \$20 million in debt. The investment bank charges a 5% fee for issuing equity. No fee applies to debt issuance. The required interest rate on debt is 4%. The expected return on levered equity is 15% Ciao plans to keep a constant debt-to-equity ratio equal to 64.52%. The perpetual EBIT of the project is \$7 million a year and there is no asset depreciation. The corporate tax rate is 25%.

What is the NPV to equity holders of the project?

The correct answer to this should be \$3.09 million.

However, I have been trying to figure out how to solve it. There is no information on wether or not the floatation costs for equity are tax deductible, if they should be discounted and written off through the lifetime of the project or in the first period. There is also no explicit information on the cost of the project, if the floatation cost is from the gross proceedes or not. If I had gotten this for a multiple choice exam, I’d flip out, because I feel that the problem is not well written, hence it will give tons of frustration!

If someone is able to solve it I’d appreciate it, as this is probably going to keep me up all night.

this is in L3?

I agree with Alladin, this looks like a LV 2 problem. What study section is this supposed to apply to?

May be the problem should be cracked like this (with some rounding).

1. To discount EBIT in perpetuity you need to find the project rate of return. Thus, the equation is

Kequity = K project + 0.6452 x {K project - K debt};

15% = X + 0.6452 (X - 4%); and you have got K project = 10.7% for discounting the EBIT cash inflow.

1. PV of cash inflow is (7 mln x [1 - 0.25])/0.107 = 49.07 mln

2. PV of cash outflow, or investments, is (Equity cost = 26 mln PLUS Debt = 20 mln) = 46 mln.

3. NPV = 49.07- 46 = 3.07 mln.

However, i doubt this approach because cash flows must be discounted using WACC. The problem provides only EXPECTED return on equity instead of required one. It seems floating costs are included into a 15% return on levered equity.