Question

Acme has branched out to rentals of office furniture to start-up companies. Consider a $4,100 desk. Desks last for six years and can be depreciated immediately. Assume that lease rates for old and new desks are the same and that Acme’s pretax administrative costs are $310 per desk at the beginning of each year. The cost of capital is 12% and the tax rate is 21%. Lease payments are made in advance, that is, at the start of each year. The inflation rate is zero. Suppose a blue-chip company requests a six-year financial lease for a $4,100 desk. The company has just issued five-year notes at an interest rate of 9% per year. What is the break-even rate in this case? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

PLEASE PROVIDE EXCEL SHEET WITH EXPLANATION

Answer 1

Step 1:

Lets find the Net Present Value of all cash-flows except the lease rental:

Notes:

1. Cost of $4,100 = given in question

2. Desk to be depreciated immediately. Hence full depreciation for desk value $4,100 to be taken in Year 0. Tax shield of 21% on $4,100 for $861 to be considered as cash-inflow in year 0

3. Administrative costs = $310

Post tax administrative costs = $310*(100%-21%) = $245. These are incurred at the beginning of each year , hence from Year 0 to Year 5.

4. Annual cash flow = Cost + Post tax administrative costs - Tax shield on Depreciation

5. Discount factor at 12% =

Year 1 = 1/(1+12%)^1 = 0.893

Year 2 = 1/(1+12%)^2 = 0.797

Year 3 = 1/(1+12%)^3 = 0.712

Year 4 = 1/(1+12%)^4 = 0.636

Year 5 = 1/(1+12%)^5 = 0.567

6. Present Value of Annual Cash-flow = Annual cash flow * Discount factor at 12%

Working:

Step 2: Break even rate

Annual leases are made in advance. Hence lease payments will be received from Year 0, Year 1 to Year 5.

To have break-even rate, the present value of after tax annual leases of 5 years at 12% should equal $4,366.71.

Let Annual lease payment be X. Tax rate is 21%. Hence after tax annual lease = X*(100%-21%) = X*79% = 0.79X

Cumulative discount factor for 5 years at 12% discount rate = ((1-(1+12%)^-5))/12% = 3.60478

Thus, the present value of after tax annual leases of 5 years at 12% = 0.79X * 3.60478 = 2.84777X

Annual lease paid at year 0 = 0.79X*1 = 0.79X

Hence, 2.84777X+0.79X = 4,366.71 =

3.63777X = 4,366.71=

X = 4,366.71/3.63777 = $1,200.38

Thus, the break-even rate is $1,200.38