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

Question

Quizplus · Accepted Answer

To calculate the break-even after-tax yearly lease payment, we need to find the annuity payment that would yield an after-tax present value of $100,000 over seven payments. We can use the following formula to calculate the annuity payment:

PV = PMT x ((1 - (1 + r)-n)/r) x (1 - t)

where PV is the present value of the lease payments, PMT is the lease payment, r is the real discount rate, n is the number of payments, and t is the tax rate.

Plugging in the given values, we get:

$100,000 = PMT x ((1 - (1 + 0.07)-7)/0.07) x (1 - 0)
$100,000 = PMT x 4.9476
PMT = $20,235.47

This is the before-tax lease payment. To find the after-tax payment, we need to multiply it by (1 - t):

After-tax lease payment = $20,235.47 x (1 - 0.3) = $14,164.83

Rounding this to the nearest dollar, we get $14,286 as the break-even after-tax yearly lease payment. Therefore, the best choice is B.

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