QUESTION 1

Today is Nasrul 30th Birthday. Five year ago Nasrul open an investment account when he inherited RM 200,000 from grandmother on his 25th birthday. Nasrul added RM 3000 to this account on his 27th birthday ,RM 4000 on her 28th birthday and RM 5000 on her 29th birthday. His goal is to have RM 1 million in the account on her 40 th birthday.This investment accout has earned and will continued to earned return 12% per year

To achieve this goal he plan to contribute a fixed amount to the account each year on his birthday. He will make 11 equal contribution starts today and the final contribution will occur on his 40th birthday.

However Nasrul currently has outstanding loan with bank ABC when he purchase his home 3 years ago on his 27th birthday. The Loan amount was RM 120,000 for 20 years at an interest of 6% compounded semi-annually. Thus far Nasrul has been paying for the house on instalment basis every six month. This Morning Nasrul just came back from the bank after paying his sixth instalment payment and the bank officer has provided his with loan amortization schedule. After looking at the amount outstanding he now plan to withdraw some money from his investment account to settle this outstanding balance immediately.

In addition he also plan to withdraw RM 20,000 from account on his 35 th birthday to finance the down payment on his dream car

a) Given all the Deposit that he has made so far how much Nasrul should have in his investment account today

b) How much was Nasrul’s instalment payment for his home loan with bank ABC?c) Based on loan amortizartion schedule how much should NAsrul withdraw from his

investment account to pay off outstanding balance on his home loan today d)Taking into account all his deposits and his withdrawls until he celebrate his 40th birthday how large does each of these 11 equal contribution have to be for Nasrul’s investment account to reach RM 1 million

Question 2A) You are considering a security with the following possible rates of return: Probability Return (%) 0.20 9.6 0.30 12.0 0.30 14.4 0.20 16.8a. Calculate the expected rate of return. (2.5 MARKS)

a) a. R = (0.2)(9.6) + (0.3)(12.0) + (0.3)(14.4) + (0.2 )(16.8) = 13.2%

b. Calculate the standard deviation of the returns. (2.5 MARKS)

b. s(R) = [(9.6 - 13.2)2 (0.2) + (12 - 13.2)2(0.3) + (14.4 - 13.2)2(0.3) + (16.8 - 13.2)2(0.2)]1/2 = 2.459%

B) Security A has an expected rate of return of 22% and a beta of 2.5. Security B has a beta of 1.20. If the Treasury bill rate is 10%, what is the expected rate of return for security B?

(5 MARKS)b) RA = RF + BA(Rm - Rf) .22 = .10 + 2.5 (Rm - .10) .12 = 2.5 (Rm - .10) = 2.5 Rm - .25 .37 = 2.5 Rm .148 = Rm

RB = Rf + BB(Rm - Rf)RB = .10 + 1.20(.148 - .10)RB = .1576

C) Asset A has a required return of 18% and a beta of 1.4. The expected market return is 14%. What is the risk-free rate?

(5 MARKS)

c) K = Krf + (Km-Krf)b18% = X + (14% - X)1.418% - X =19.6% - 1.4X.4X = 1.6%X = 4% = Risk-free Rate = Krf

Question 3A)Sunrise Sdn. Bhd. plans to accumulate funds to provide a retirement package for its President of Research, Jill Moran. Jill Moran by contract will retire at the end of 12 years. Upon retirement, she is entitled to receive an annual payment of $42,000 for the period of 20 years. If she dies prior to the end of the 20-year period, the annual payments will be passed to her heirs.

During the 12 year “accumulation period” Sunrise wishes to fund the plan by making equal annual deposits into an account earning 9% interest. Once the 20-year “distribution period” begins, Sunrise plans to move the accumulated fund into an account earning 12% annually. At the end of the distribution period, the account balance will equal to zero. The first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

You are required to:

i. draw and label a time line depicting all the cash flows associated with Sunrise’s view of the retirement plan.

ii. calculate how large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity.

PVA = $42,000[(1-(1.12)-12)/0.12] = $313,717

iii. calculate how large must Sunrise’s equal annual deposits into the account be over the 12-year accumulation period to fund Ms. Moran retirement package.

313,717 = PMT[(1.09)12 – 1/0.09]

Cash inflow:Accumulation Period

12 end-of-year deposits@ 9% annually

Cash outflow:Distribution Period

20 end-of-year payments of RM42,000 @ 12% annually

PMT = RM15,576.26

iv. calculate how much would Sunrise have to deposit annually during the accumulation period if Ms. Moran retirement package has an infinite life.

PVperp = PMT / i = RM42,000 / 0.09 = RM466,667.

Annual deposit during accumulation period:466,667 = PMT[(1.09)12 – 1/0.09]PMT = RM23,170.00

B) What are the monthly mortgage payments if Mr. Ahmad takes a four-year loan for RM10,000 at 12% interest per annum? If after four months, Mr. Ahmad decides to pay off his loan, how much is the balance? Solution

i = 12% ÷ 12 = 1%; n = 4 12 = 48

PVA = PMT [1-(1+i)-n]/iPMT = 10,000 ÷ [1-(1.01)-48]/.01PMT = RM263.37 monthly

MONTH BEG. BAL PMT INT PRIN. RED END BAL1 10,000 263.37 100 163.37 9,836.632 9,836.63 263.37 98.37 165.00 9,671.633 9,671.63 263.37 96.72 166.65 9,504.984 9,504.98 263.37 95.05 168.32 9,336.66

Loan balance after four months = $9,336.66