If the after-tax present value of buying equipment and using it for 6 years is $100,000, calculate the break-even after-tax yearly lease payment (7 payments) using 7% discount rate. (Assume that the lease payments are made at the beginning of the year.)

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The after-tax present value of buying equipment is the same as the after-tax present value of leasing the equipment. This means:

PV of buying the equipment = PV of leasing the equipment

We know that the PV of buying is $100,000. To find the PV of leasing, we need to calculate the annual payments first:

PV of leasing = annuity factor x annual payment

Annuity factor = (1 - 1/(1+discount rate)^n)/discount rate
Annuity factor = (1 - 1/(1+0.07)^7)/0.07 = 5.0336

PV of leasing = 5.0336 x annual payment

We want to find the annual payment that will make the PV of leasing equal to $100,000:

5.0336 x annual payment = $100,000
Annual payment = $100,000/5.0336 = $19,870.45

However, this is the before-tax amount. To find the after-tax amount, we need to adjust for the tax shield on lease payments. Assuming a tax rate of 40%:

After-tax annual lease payment = before-tax annual lease payment x (1-tax rate)
After-tax annual lease payment = $19,870.45 x (1-0.4) = $11,922.27

This is the annual payment that would make the PV of leasing equal to $100,000 after tax. However, we need to find the break-even after-tax yearly lease payment, which is the amount that would make the PV of leasing equal to the PV of buying ($100,000). Assuming the same tax rate of 40%, we can use the formula:

Break-even after-tax annual lease payment = PV of buying/annuity factor x (1-tax rate)
Break-even after-tax annual lease payment = $100,000/5.0336 x (1-0.4) = $17,341.04

Therefore, the break-even after-tax yearly lease payment is $17,341, which is closest to option B.

If the After-Tax Present Value of Buying Equipment and Using