Financial Math Answers

Suppose that ABC Ltd is considering purchasing one of three new processing machines. Either machine would make it possible for the company to produce its products more efficiently.
Estimates regarding each machine are provided below:

Machine A Machine B Machine C
Original cost $79,000 $110,000 $244,000
Estimated life 7 years 8 years 10 years
Salvage value Nil Nil $30,000
Estimated annual cash inflows $30,000 $ 60,000 $58,500
Estimated annual cash outflows $ 7,000 $ 35,000 $18,500

C. Calculate the internal rate of return for Machine A? [Hint: internal rate of return is the rate which results in a zero NPV using linear interpolation], and discuss 1 drawback of the IRR against the NPV

Suppose that ABC Ltd is considering purchasing one of three new processing machines. Either machine would make it possible for the company to produce its products more efficiently.
Estimates regarding each machine are provided below:

Machine A Machine B Machine C
Original cost $79,000 $110,000 $244,000
Estimated life 7 years 8 years 10 years
Salvage value Nil Nil $30,000
Estimated annual cash inflows $30,000 $ 60,000 $58,500
Estimated annual cash outflows $ 7,000 $ 35,000 $18,500



A. If the projects cannot be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital?


B. If the projects can be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital?

Explain in a paragraph of about 100-150 words when and why would a bond be sold on a premium or discount? You may use graphs, equations, or other aids to assist your explanation.

Let ρ =( w1,w2) be a portfolio of two securities. Find the value of w1and w2 in the following situations:
i) p12 = -1 and ρ is risk-free.
ii) σ1 = σ2 and variance P is minimum.
iii) Variance on P is minimum and ρ12 = -0.5 , σ1 = 2 and σ2 = 3.

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house? (1 mark)
B. Find the value of the monthly payment? (3 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks)

II. Fill out the loan amortization schedule provided in the solution template for the first 5 loan payments. What do you notice about the composition of the payment amount? (6 marks)

II. Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.

the present value of an annuity of $2000 payable at the start of each month at J12 = 12% for 8 years is:

Your best friend John is willing to sell his brand new car to you at a negotiated price which he is willing to keep unchanged for 15 years. You have paid $5,000 to John to lock the deal. However, you still need to pay $20,000. If you could invest the rest of your savings of $8,000 at an annual interest rate of J1 = 5%, how much money can you accumulate within 15 years and would you be able to buy his car?

Tele-Reco is a new specialty store that sells mobile phones, laptops and other computer accessories. A new Japanese-manufactured mobile phone reorder costs Tele-Reco $600 per unit. Tele-Reco’s annual holding cost rate is 22%. Ordering costs are estimated to be $70 per order.

QUESTION 2: LOAN AMORTIZATION [35 MARKS]

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house? (1 mark)
B. Find the value of the monthly payment? (3 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks)