ACFI2070 Individual Assignment-1

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Finance

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May 15, 2024

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ACFI 2070 Business Finance Problem Set (50 marks) [This problem set contributes 25% to your overall mark in this course.] [You should answer all the questions.] Question 1 (12 marks) Five years ago, Mike borrowed a home loan of $500,000, repayable by equal monthly instalments over 20 years. At the time he borrowed the money, the interest rate was 4 .8% per annum, compounding monthly. The general level of interest rates has been rising recently and the bank has now decided to increase the interest rate to 6.6% per annum, compounding monthly. a) What is the original monthly repayment when interest rate is 4.8% p.a. compounding monthly? ( 3 marks) The interest rate i= 4.8% p.a. compounding monthly => the effective monthly rate i= 4.8%/ 12= 0.4% The original monthly repayment: Where P= $500,000 n= 12*20=240 i=0.4%  C=3244.79 So, Mike will need to repay $3,244.79 per month with the original interest rate 4.8% p.a. compounding monthly. b) What is the balance owing now? ( 3 marks) Mike borrowed a home loan of $500,000 5 year ago => Mike has made 60 payments (12* 5 years = 60 months) => Mike will need to have another 180 repayments (rest 15 years) Where C=3244.79, n=180 i=0.4%.  P= $415,777.8 After 5 years, the balance Mike owing is $415,777.8. c) If the loan term is to remain unchanged, what will be the new monthly repayment when interest rate increases to 6.6% p.a. compounding monthly? ( 3 marks)

The new monthly repayment when interest rate 6.6% p.a. compounding monthly => the new effective monthly rate i=6.6%/12 = 0.55%. If the loan term is to remain unchanged => 180 repayments to pay off the loan (rest 15 years) => n= 180 The new monthly repayment: Balanceowing = C new i new ∗( 1 − 1 ( 1 + i new ) n ) $ 415,777.8 = C new 0.55% ∗( 1 − 1 ( 1 + 0.55% ) 180 ) C new =3644.77 So, Mike will need to repay $3,644.77 per month with the new interest rate 6.6% p.a. compounding monthly. d) If the monthly payment is unchanged, how many months will the loan term increase when interest rate increases to 6.6% p.a. compounding monthly? ( 3 marks) If the monthly payment is unchanged => C=3244.79, effective monthly rate i= 0.55% The new loan term (n): Balanceowing = C ❑ i new ∗( 1 − 1 ( 1 + i new ) n ) $ 415,777.8 = 3244.79 0.55% ∗( 1 − 1 ( 1 + 0.55% ) n ) n new =222.42 or ~ 223 repayments to pay off the loan or 223 months  When raising the interest rate to 6.6% p.a compounding monthly, Mike will need to pay extra: 223- 180 = 43 monthly repayments to pay off the loan. Question 2 (12 marks) James purchases a five-year government bond which makes annual coupon payments of 4% and offers a yield of 4.5% annually compounded. The face value of this government bond is $1000. Suppose one year later the bond yields drops to 3.25%, James decides to sell the bond in the market. a) What is the price of this five-year government bond when it is issued? ( 4 marks)

James purchases a five-year government bond with the face value FV= $1000. This government bond makes annual coupon payments of 4% p.a. => Annually coupon payment C = $1000 x 4% = $40 Number of coupon payments until maturity n= 5. Market interest rate (yield) i= 4.5% p.a The price of this bond when it is issued: b) What is the price of this bond one year later? ( 4 marks) One year later the bond yields drop to 3.25% p.a => new i=3.25% p.a. Number of coupon payments until maturity n= 4. The price of this bond at one year later (when the bond yields drop): c) What return will James earn for this 12-month investment? ( 4 marks) James earns for this 12-month investment: (Sold price – Purchased price) + 1 year coupon payment.  ($1,027.71- $978.05) + (4% x $1,000) = $89.66 Question 3 (14 marks) Healthy. Ltd is considering a proposal to produce organic food. It will involve an initial investment of $80,000. In each of years 1 to 10, the project is estimated to produce sales of $60,000 with sales volume of 5,000 and to incur total variable costs of $25,000 and fixed costs of $15,000. The cost of capital is 10%. a) Calculate the NPV of this project. ( 4 marks) P = C i ¿ P = $ 40 4.5% ¿ P = C i ¿ P = $ 40 3.25% ¿

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Variable Estimated Cost of capital 10% Sales revenue 60,000 $ Total variable cost 25,000 $ Sales volume 5,000 Fixed operating cost 15,000 $ Initial cash outlay 80,000 $ Selling price (perunit) 12 $ Sales revenue/Sales volume Year 0 1 2 3 4 5 6 7 8 9 10 Sales revenue 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ Variable Cost 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ 25,000 -$ Fixed Operating cost 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ 15,000 -$ Initial Cash outlay 80,000 -$ FCF 80,000.00 -$ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ 20,000.00 $ PV of FCF 80,000.00 -$ 18,181.82 $ 16,528.93 $ 15,026.30 $ 13,660.27 $ 12,418.43 $ 11,289.48 $ 10,263.16 $ 9,330.15 $ 8,481.95 $ 7,710.87 $ NPV 42,891.34 $ b) What is the break-even level of sale price per unit? ( 10 marks) Goal seeks function: At the break-even point  NPV = 0 Variable Estimated Cost of capital 10% Sales revenue 53,019.63 $ Total variable cost 25,000 $ Sales volume 5,000 Fixed operating cost 15,000 $ Initial cash outlay 80,000 $ Selling price (perunit) 10.60 $ Question 4 (12 marks) The following table outlines the information for 3 risky assets. Assume the correlation between the returns on assets A and B is 0.5, the correlation between the returns on assets A and C is 0.2 and the correlation between the returns on assets B and C is -0.3 a) If you are considering an equally weighted portfolio of A and B, calculate the portfolio’s expected rate of return and standard deviation of rates of return. ( 5 marks) b) If you are considering an equally weighted portfolio of A, B and C, calculate the portfolio’s expected rate of return and standard deviation of rates of return. ( 5 marks) A B C Expected return E(R) % 6% 10% 15% Risk (σ %) 2% 5% 7%

c) Based on the results from a) and b), which equally weighted portfolio will a rational investor prefer? ( 2 marks)

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