UESTION 1 [40 MARKS]

1. An investor puts 5,000 in a savings account that pays 10% compound interest at the end of each year. Compare how much the investor would have after 6 years if the money was:

(i) Invested for 6 years

(ii) Invested for 3 years, then immediately reinvested for a further 3 years.

2. A company is due to receive a payment of 500,000 from a customer in 6 months time. To smooth its cashflows, the company would prefer to receive the payment immediately, and has agreed to transfer its entitlement to this payment to a third party (a discount house) in return for an immediate payment calculated using a rate of commercial discount of 16% per annum.

How much will the immediate payment made by the discount house be?

3. Find the present value of:

(i) a series of investment of $1 at the end of each year for 25 years with effective

interest rate of 13.5% p.a.; and

(ii) a series of investment of $1 at the beginning of each year for 15 years with

effective interest rate of 13.5% p.a.

4. 250 is invested in a savings account. The nominal rate of interest convertible monthly for the first 3 months is 18% and the nominal rate of interest convertible quarterly for the next 9 months is 20%. How much is in the account at the end of the year?

5. The force of interest is given by:

()= {0.01+0.01 0<40.150.0032 4<60.06 6

(i) Find the expression for the value at time =0 of a payment of $100 at time .

(ii) A payment of $100 is received at time 3 and a further payment of $250 is

received at time 5. Calculate the accumulated value of these payments at time 8.

(f) Use the Black-Scholes-Merton model to calculate the value of a European call option on an asset priced at $68.50. The exercise price is $65, the continuously compounded risk-free rate is 4%, the options expires in 110 days, and the volatility is 0.38. There are no cash flows on the underlying.

(g) For a two-period binomial model, you are given the following information:

1. Each period is one year.

2. The current price for a non-dividend-paying stock is $20.

3. u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up.

4. d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down.

5. The continuously compounded risk-free interest rate is 5%.

Calculate the value of an American call option on the stock with a strike price of $22

h)R delegates all the development work to outside companies. The estimated cashflows for Project R are (where brackets indicate expenditure):

contractors fees Beginning of Year 1 (150,000)

contractors fees Beginning of Year 2 (250,000)

contractors fees Beginning of Year 3 (250,000)

Sales End of Year 3 1,000,000

Project S carries out all the development work in-house by purchasing the necessary equipment and using the companys own staff.

The estimated cashflows for Project S are:

New equipment Beginning of Year 1 (325,000)

Staff Cost Continuous payments Through Year 1 (75,000)

Staff Cost Continuous payments Through Year 2 (90,000)

Staff Cost Continuous payments Through Year (120,000)

sales End of Year 3 1,000,000

REQUIRED

(i) Calculate the net present value for Project R and Project S using a risk discount

rate of 20% per annum. Using net present values as a criterion, which project

is preferable?

(ii) Find the internal rate of return for Project R

2. Mr. Ali enters into a 6-month forward on Microsoft Stock (No dividend has been forecasted in the future). It is currently trading at $100 per share and the continuous rate is 5% per year. What is the forward price?

After 3 months, the last traded price is $120 per share. What is the price of a 3- month forward now? Elaborate the strategy that Ali could chose to make a profit.

3. On 01 January 2018, the balance in account is $25,200. On 01 April 2018, $500 are deposited in this account and on 01 July 2019, a withdrawal of $1,000 is made. The balance in the account on 01 October 2019 is $25,900. Compute the annual interest rate in this account using the dollar-weighted method?

4. For an investment account, you are given the following

Date	1/11/17	1/3/18	1/8/18	1/2/19	1/4/19
Balance prior deposit or withdrawal	$14,516	$14,547	$18,351	$16,969	$18,542
Deposit	-	$3,000	-	$2,500	-
Withdrawal	-	-	$2,000	-	-

1. A loan of 100,000 is repayable by equal semi-annual payments for 4 years. The effective rate of interest is 7% p.a.

REQUIRED

(i) Find the equal semi-annual payment amount.

(ii) Construct an amortization schedule for the loan repayment.

(iii)What is the interest portion paid on the 5th payment?

(iv) What is the total interest paid after the 7th payment?

e) The force of interest is given by:

()= {0.01+0.01 0<40.150.0032 4<60.06 6

(i) Find the expression for the value at time =0 of a payment of $100 at time .

[9 Marks]

(ii) A payment of $100 is received at time 3 and a further payment of $250 is

received at time 5. Calculate the accumulated value of these payments at time