Financial Math Answers

Stark is seeking to hold his $20,000 savings in a savings account for 1 year. He enquires with three banks, Bank A, Bank B, and Bank C. Bank A offers J12 = 12%; Bank B offers J2 =12.1%, and Bank C offers J4 = 12.05%. Which bank should Stark deposit his savings?

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? (9 marks)

B. If the projects can be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (6 marks)

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 (5 marks)

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

Payment Number Beginning Loan Balance Payment Amount Interest Expense Principal Repayment Ending Loan Balance
1
2
3
4
5
b. also find the Ending Loan Balance Working Space for each payment:

III. Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.:

A. Convert the interest rate J2=9% to J12 equivalent

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)

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.

Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.

Convert the interest rate J2=9% to J12 equivalent
Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate?
Assuming that the family seeks to continue their initial monthly payment, calculated in part I, how many full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later?

Explain in a paragraph of about 100-150 words when and why would a bond be sold on a premium or discount?

Isaac wants his fiancee to make 14 half-yearly withdrawals starting now. He wants the first withdrawal to be R900, and subsequent withdrawals to increase by 9% every six months. Interest is earned at 8% pa compounded half-yearly.

How much will Isaac’s fiancee withdraw in total?

)The office manager for the Gotham Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6,500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company:
Order Quantity (boxes) Price per box ($)
200-999 16
1,000-2,999 14
3,000-5,999 13
6,000+ 12

Determine the optimal order quantity and the total annual inventory cost.
c)Determine the optimal order quantity and the total annual inventory cost, if the carrying cost is 20% of the price of a box of stationery.