ICAP PRC-2 Financial mathematics: practice questions with answers

Question 1

Ayesha Rafiq, a Lahore schoolteacher, has Rs 800,000 to place on deposit for 4 years. Her bank offers either 11% a year simple interest or 11% a year compounded annually, with all interest paid at the end of the 4 years. By how much does the interest from the compound option exceed the interest from the simple option (to the nearest rupee)?

1. A Rs 352,000
2. B Rs 414,456
3. C Rs 62,456
4. D Rs 1,214,456

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Answer: C. Simple interest = P x r x t = 800,000 x 0.11 x 4 = Rs 352,000.

Compound amount = 800,000 x (1.11)^4 = 800,000 x 1.51807 = Rs 1,214,456, so compound interest = 1,214,456 - 800,000 = Rs 414,456.

Extra interest from compounding = 414,456 - 352,000 = Rs 62,456. The difference is the interest earned on interest: simple interest is calculated on the original principal only, while compound interest is added to the balance each year and earns interest itself.

Question 2

Saima Qureshi pays Rs 60,000 into a savings plan at the start of each year for 6 years (6 payments, the first today). The plan pays 10% a year, compounded annually. The future value of Re 1 per period at 10% is 7.71561 for 6 periods and 9.48717 for 7 periods (values for an ordinary annuity, payments at the end of each period). What will the plan be worth at the end of year 6 (to the nearest rupee)?

1. A Rs 509,230
2. B Rs 462,937
3. C Rs 569,230
4. D Rs 360,000

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Answer: A. Payments at the start of each year form an annuity due. Each payment is invested for one more year than in an ordinary annuity.

FV (ordinary) = 60,000 x 7.71561 = Rs 462,936.60

FV (annuity due) = 462,936.60 x 1.10 = Rs 509,230.26 = Rs 509,230 (to the nearest rupee).

Alternative route: annuity-due factor = (7-period factor - 1) = 9.48717 - 1 = 8.48717; 60,000 x 8.48717 = Rs 509,230.20 = Rs 509,230.

Question 3

Indus Builders, Hyderabad, will receive Rs 2,500,000 from a customer at the end of 6 years. Its required return is 9% a year. Extract from the present value (discount factor) table at 9%: year 5 0.650; year 6 0.596; year 7 0.547. What is the present value of the receipt (to the nearest rupee)?

1. A Rs 1,625,000
2. B Rs 1,150,000
3. C Rs 1,367,500
4. D Rs 1,490,000

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Answer: D. PV = S / (1 + r)^n = S x discount factor.

The receipt is at the end of year 6, so use the 9%, 6-year factor of 0.596.

PV = 2,500,000 x 0.596 = Rs 1,490,000.

Question 4

Zarnab Foods appraises all new projects by discounting their cash flows at 13% a year. Which of the following best describes what this 13% represents?

1. A The minimum return that the providers of finance require, so it is the opportunity cost of the funds used
2. B The rate of general price inflation expected over the life of the projects being appraised
3. C The internal rate of return that each project must be expected to earn over its life
4. D The interest rate that the company receives on its surplus cash held in short-term deposits

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Answer: A. In discounted cash flow appraisal the discount rate is the cost of capital (required rate of return): the return the company's providers of finance expect, which is the opportunity cost of tying funds up in the project.

A project whose cash flows, discounted at this rate, have a positive NPV earns more than investors require and adds to their wealth. The IRR is a project-specific result that is compared with the cost of capital; it is not the rate used to discount.

Question 5

Thar Ceramics is comparing two projects, each costing Rs 5,000,000 now. Both produce identical cash inflows in years 1 to 3, and both have a payback period of exactly 3 years. Project Y also produces Rs 2,000,000 a year in years 4 and 5; Project X produces nothing after year 3. Which statement about the payback method is correct?

1. A Payback favours Project Y because it produces Rs 4,000,000 more cash in total
2. B Payback favours Project X because it stops producing cash at the end of year 3
3. C Payback ranks the projects equally because it ignores cash flows after the payback point
4. D Payback ranks the projects equally because it discounts all flows at the same rate

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Answer: C. The payback period measures only how long it takes to recover the initial outlay from undiscounted cash inflows. Both projects recover Rs 5,000,000 in exactly 3 years, so payback ranks them equally.

Two limitations are shown here:
- payback ignores all cash flows after the payback point (Y's Rs 4,000,000 in years 4 and 5), so it cannot see that Y is clearly better; NPV would include those flows;
- simple payback also ignores the time value of money, because it adds rupees from different years without discounting.

Question 6

A Jhelum furniture maker calculates that a new spray-finishing line has a net present value of +Rs 412,000 when its cash flows are discounted at the company's 12% cost of capital. Which of the following statements is correct?

1. A The line will earn a total accounting profit of Rs 412,000 over its life
2. B The line returns more than 12% a year, so accepting it adds Rs 412,000 of value today
3. C The line's internal rate of return is 12% plus the NPV as a percentage of the outlay
4. D The line's NPV would be higher than Rs 412,000 if discounted at 15% instead of 12%

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Answer: B. NPV = present value of cash inflows - present value of outflows, both at the cost of capital.

A positive NPV of Rs 412,000 means that, after allowing for the 12% return that providers of finance require, the project still produces a surplus worth Rs 412,000 today. The project therefore earns more than 12% (its IRR is above 12%) and should be accepted.

NPV measures cash in today's money, not accounting profit; and for a conventional project a higher discount rate gives a lower NPV.