Question

1. You are opening a carnival. Building the carnival will cost $15M dollars, and the carnival will produce EBIT of $3M per year for the foreseeable future. Your tax rate is 28%, your cost of unlevered equity is 11%, and your cost of debt is 6%. In order to boost teen employment, the State of Kansas is offering you an $8M perpetual loan with an interest rate of 5%, but applying for this loan will incur administrative costs of $500,000.

A) What is the NPV of this amusement park if you do not accept the loan?

B) What is the NPV of the loan you are being offered?

C) What is the NPV of this project using the APV method?

Answer 1

A) If you don't accept the loan, then the whole initial cost of the amusement park will be funded by equity. Hence, Unlevered cost of equity of 11% will be the Cost of capital used for NPV calculation.

Initial Cost = 15,000,000 | EBIT = 3,000,000 | Tax rate = 28%

NOPAT = EBIT * (1-Tax rate) = 3,000,000 * (1 - 28%) = 2,160,000

As there are no other cashflows after EBIT, other than tax, we will use the NOPAT as the free cashflow to the firm.

FCF = 2,160,000

Since EBIT is for perpetuity, hence, we will calculate its PV as a Perpetuity.

PV of Perpetuity = CF / R

R is the Unlevered Cost of Equity of 11%

PV of Cashflows = 2,160,000 / 11%

PV of cashflows = $19,636,363.64

NPV = PV of cashflows - Initial Cost

NPV of the amusement park = 19,636,363.64 - 15,000,000 = $ 4,636,363.64 or $ 4,636,364

Hence, NPV of the amusement park if you don't accept the loan is $ 4,636,364.

B) Loan amount = 8,000,000 | Rate of Interest = 5% | Administrative costs = 500,000 | Tax-rate = 28%

Interest Payment = Loan * Interest rate = 8,000,000 * 5% = $ 400,000 - To be paid perpetually

Tax Savings Due to Interest Payment =  Interest Expense * Tax rate = 400,000 * 28% = 112,000

Administrative costs to be incurred for applying = 500,000

Year 0 inflow = 8,000,000 | Year 0 Outflow = 500,000

Perpetual Inflow = 112,000 | Perpetual outflow = 400,000

PV of Interest Payments = Interest / Cost of debt = 400,000 / 5% = 8,000,000

PV of Tax Savings = Cashflow / Interest rate = 112000 / 5% = 2,240,000

NPV of the loan = Sum of all inflows - Sum of all outflows = (Loan amount + PV of tax savings) - (PV of interest Payments + Administrative costs)

NPV of the loan = 8,000,000 + 2,240,000 - 8,000,000 - 500,000 = $1,740,000

Hence, NPV of the loan is $1,740,000

C) In APV method, the final NPV is the sum of NPV calculated if the project if fully financed with equity and tax shields gained because of financing decision of debt.

APV = NPV if all equity financed + PV of Interest Tax Shield

As we have already calculated the NPV where project was fully financed with equity in Part (A), it will be the first part and we also calculated NPV of the loan in the Part (B) which will be the second part. We're using NPV of loan as it is after deduction of administrative costs which we won't have to deduct again in our APV calculation.

NPV if all equity financed = 4,636,363.64 | NPV of the loan = 1,740,000

APV or NPV in APV method = 4,636,363.64 + 1,740,000 = $ 6,376,363.64 or 6,376,364

Hence, NPV using APV method is $ 6,376,364.