Question

Your firm is considering leasing a new robotic milling control system. the lease lasts for 5 years. the lease calls for 6 payments of $300,000 per year with the first payment occurring at lease inception. the system would cost $1,050,000 to buy and would be straight-line depreciated to a zero salvage value. the actual salvage value is zero. the firm can borrow at 8%, and the corporate tax rate is 34%.what is the maximum lease payment that you would be willing to make?

a. $187,842
b. $210,307
c. $170,655
d. $175,000

Answer 1

The maximum lease payment that the firm would be willing to make is $2,051,142. Option b ($2,103,070) is the closest value.

Step-by-step explanation:

To determine the maximum lease payment that the firm would be willing to make, we need to calculate the net present value (NPV) of the lease payments and compare it to the cost of buying the system.

The annual lease payment is $300,000 for 6 years. We can calculate the NPV using the formula: NPV = ∑ (Cash Flow / (1 + Discount Rate)^n), where Cash Flow is the annual lease payment, Discount Rate is the borrowing rate adjusted for taxes, and n is the number of years.

In this case, the borrowing rate adjusted for taxes is 8% * (1 - 34%) = 5.28%. Let's calculate the NPV:

1. Year 1: $300,000 / (1 + 0.0528)^1 = $285,519
2. Year 2: $300,000 / (1 + 0.0528)^2 = $271,311
3. Year 3: $300,000 / (1 + 0.0528)^3 = $257,559
4. Year 4: $300,000 / (1 + 0.0528)^4 = $244,254
5. Year 5: $300,000 / (1 + 0.0528)^5 = $231,382
6. Year 6: $300,000 / (1 + 0.0528)^6 = $292,390

The NPV is the sum of the present values of the lease payments:

NPV = $285,519 + $271,311 + $257,559 + $244,254 + $231,382 + $292,390 = $1,582,415

The maximum lease payment that the firm would be willing to make is the amount that would make the NPV of the lease payments equal to the cost of buying the system. Using the NPV formula, we can calculate:

$1,582,415 = Cost of Buying / (1 + 0.0528)^5

By rearranging the equation and solving for the Cost of Buying, we find:

Cost of Buying = $1,582,415 * (1 + 0.0528)^5 = $1,582,415 * 1.29733 = $2,051,142

Therefore, the maximum lease payment that the firm would be willing to make is $2,051,142. Comparing this to the given options, the closest value is $2,103,070 (Option b).