Management Notes

# Management Notes

Reference Notes for Management

# The Randolph Teweles Company (RTC) has decided to acquire a new truck. One alternative is to lease the truck on a 4-year guideline contract for a lease payment of \$10,000 per year, with payments to be made at the beginning of each year.

## The Randolph Teweles Company (RTC) has decided to acquire a new truck. One alternative is to lease the truck on a 4-year guideline contract for a lease payment of \$10,000 per year, with payments to be made at the beginning of each year. Alternatively, RTC could purchase the truck outright for \$40,000, financing the purchase by a bank loan for the net purchase price and amortizing the loan over a 4-year period at an interest rate of 10% per year. Under the borrow-to-purchase arrangement, RTC would have to maintain the truck at a cost of \$1,000 per year, payable at year end. The truck falls into the MACRS 3-year class. It has a residual value of \$10,000, which is the expected market value after 4 years, when RTC plans to replace the truck irrespective of whether it leases or buys. RTC has a marginal federal-plus-state tax rate of 40%.

• a) What is RTC’s PV cost of leasing?
• b) What is RTC’s PV cost of owning?
• c) Should the truck be leased or purchased?

Solution:

Given,

Lease alternative:

• Number of period (n) = 4 years
• Lease payment (L) = \$ 10,000 payable in advance

Borrow purchase alternative:

• Purchase price (lo) = \$ 40,000
• Number of periods (n) = 4 years
• Interest rate (kd) = 10%
• Residual (salvage) value = \$ 10,000
• Depreciation = MACRS 3-year class
• Tax Rate (t) = 40%

### a) What is RTC’s PV cost of leasing?

Calculation of PV of cost of leasing

We have,

PV (L) = Lt + Lt (1-t) x PVIFAkdt, n-1 – Lt (t) PVIFkdt,n
= 10,000+ 10,000 (10.40) x PVIFA6, 4-1-Rs 10,000 (0.40) PVIF6, 4
= 10,000+ 6,000 x 2.6730- 4,000 x 0.7921
= 10,000+ 16,038 3,168.40
= 22,869.60

Therefore, the RTC’s PV cost of leasing is \$ 22,869.60.

### b) What is RTC’s PV cost of owning?

Assuming the interest payable at the end of period

• Calculation of the PMT

We have,

PVA = PMT x PVIFAkd,n
or, 40,000 PMT x PVIFA10,4
or, 40,000 PMT x 3.1699
PMT = 40,000 / 3.1699
= \$  12,618.69

 Preparation of Amortization Schedule (Amount in \$) Year Payment Interest Principal Loan balance 0 – – – 40,000 1 12,618.69 4,000 8,618.69 31,381.31 2 12,618.69 3,138.13 9,480.56 21,900.75 3 12,618.69 2,190.08 10,428.61 11,472.14 4 12,618.69 1,146.55 11,472.14

 Calculation of depreciation (Amount in \$) Year 1 2 3 4 Depreciation rate 33.33% 44.45% 14.81% 7.41% Depreciation Amount =  Dep. Rate x Purchase Price 13,332 17,780 5,924 2,964

Now, Calculation of PV of cost of buying Hence, the present value of the purchasing is \$ 23,036.81.

### c) Should the truck be leased or purchased?

The present value of the cost of buying is less than the present value of the leasing .Therefore, the firm should acquire the new truck rather than taking on lease.