## 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 (l
_{o}) = $ 40,000 - Number of periods (n) = 4 years
- Interest rate (k
_{d}) = 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) = L_{t} + L_{t }(1-t) x PVIFA_{kdt, n-1} – L_{t} (t) PVIF_{kdt},_{n}

= 10,000+ 10,000 (10.40) x PVIFA_{6, 4-1}-Rs 10,000 (0.40) PVIF_{6, 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 PVIFA_{kd},_{n}

or, 40,000 PMT x PVIFA_{10,4}

or, 40,000 PMT x 3.1699

PMT = 40,000 / 3.1699

= $ 12,618.69

| ||||

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 |

| ||||

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.