Question

RussEll MK (a) Mr Muzungu is running a sole proprietorship business which he inherited from his father several years ago. As part of his expansion plans, he intends to get a motor vehicle to be used to run several errands, as the current car he uses, is shared between himself and his wife. He has been advised by his colleague that he should get a motor vehicle loan from one of the top banks. The motor vehicle he intends to purchase will cost K250,000.00 and he reckons to finance it 100 percent through a loan. The loan is to be paid in equal semi-annual payments for a period of three years at an annual interest rate of 16 percent. He is concerned about meeting the semi- annual payments from his business cash flows which fluctuate from time to time, He has asked you to draw up an amortization schedule showing the semi-annual payments to be made on this loan, which he can use for cash flow purposes. QUESTION FOUR (Ignore transaction fees, commissions and other upfront fees for accessing the loan) (15 marks) b) Chunga and Company trade in golf clubs. They sale the clubs either through cash or through a lease facility with their clients. You have recently started playing golf and want to lease a set of golf clubs from Chunga and Company. The lease contract is in the form of 24 equal monthly payments at a 10.4 percent stated annual interest rate. compounded monthly. Because the clubs cost K3,500 retail, Chainama wants the present value of the lease payments to equal K3,500. Suppose that your first payment is due immediately. What will your monthly lease payments be? (10 marks) Total (25 marks)

Answer 1

As there are multiple questions, only the first questions is being answered below:

Loan Amount (P) =  K 250,000.00 (100% financed, hence we are taking the full amount)

Interest Rate = 16% per annum. As we will make half yearly payments, half yearly interest (R) = 16%/2 = 8 %

Duration of loan = 3 years. Since the payments are semi-annual, total number of payments made (N) = 3 * 2 = 6

The formula to calculate semi-annual payments =

(P * R * (1+R)^N ) / ((1+R)^N - 1)

Substituting the given values, we get

(250,000 * 0.08 * (1+0.08)⁶ ) / ((1+0.08)⁶ - 1) = 31,737.49 / 0.5869 = 54,078.85

The semi-annual payment to be made on the loan is K54,078.85