Financial Math Answers

A furniture manufacturer makes two types of furniture – chairs and sofas. The production of the sofas and chairs requires three operations – carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The profit per chair is $90 and the profit per sofa is$75.

Use graphical method to recommend an optimalproductionplan (8marks)

Discuss any three assumptions that you may have considered in formulating the productionplan

Daniel is a successful businessman. Recently, he purchased a bungalow house. He purchased 

the house at a price of 1.23 million. He paid 10% of the price of the house as a down payment. 

He borrowed from a bank to settle the balance. He agreed to pay the loan by making monthly 

instalments for 30 years at the rate of 2.98% compounded monthly.

(a)

Find the down payment amount and loan amount. Hence, calculate the monthly 

payment for the loan.

(b)

What will be the total interest paid by Daniel?

(c)

What will be the total amount paid by Daniel for the house?

(d)

If Daniel missed the first two monthly payments, how much has he to pay the third 

payment to settle all outstanding arrears?

(e)

Find the effective rate which is equivalent to the above to the above nominal rate. 

(C) An investor is considering two projects A and B. Project A involves the investment of £1 million at the outset. The only income to be received will be a payment of £3.5 million after ten years. Project B also involves the investment of £1 million at the outset. Income will be received from this project continuously. In the first year the rate of payment will be £0.08 million, in the second year £0.09 million, in the third year £0.10 million, with the rate increasing by £0.01 million each year thereafter until the tenth year, after the end of which no further income will be received.

(a) Calculate the net present value of both investment projects at a rate of interest of 4% per annum effective.

(b) Show that the discounted payback period of project A is after that of project B (no further calculation is necessary).

(c) In the light of your answer to (i) above, explain which project is the more desirable to an investor with unlimited capital, and why. 

(C) An individual purchases a car for $15,000. The purchaser takes out a loan for this amount that involves him making 24 monthly payments in advance. The annual rate of interest is 12.36% per annum effective. Calculate the flat rate of interest on the loan.

(D) (a) A forward contract with a settlement date at time T is issued based on an underlying asset with a current price of B.

The annualised risk-free force of interest applying over the term of the forward contract is δ and the underlying asset pays no income. Show that the theoretical forward price is given by K = BeδT , assuming no arbitrage.

(b) An asset has a current market price of 200P , and will pay an income of 10P in exactly three months’ time. Calculate the price of a forward contract to be settled in exactly six months, assuming a risk-free rate of interest of 8% per annum convertible quarterly. 

(A) A fixed interest security of nominal amount K100,000 will be repaid at 110% after15 years. The security bears a coupon of 9% p.a. payable annually in arrears.

(i) On the issue date the security is purchased for K80,000 by an investor who is liable to income tax at 40% and to capital gains tax at 30%. Find the investor’s net (meaning after tax) effective redemption yield p.a. for the transaction.

(ii) The investor wishes to secure an after-tax redemption yield of 9% p.a. Determine how much the investor should pay for the security.

(B) Investors often allow for risk by requiring a higher yield to lend money to a borrower who is thought to be at higher risk of not repaying some or all of the interest and capital. Explain the consequences for companies or governments trying to raise money in the capital markets.