Risks and returns

Section 2 of Module 12 (up to 20% of the paper) is calculation-heavy: present values, the capital budgeting rules (NPV, IRR, payback, profitability index), expected return and standard deviation, and return measures (holding-period, arithmetic and geometric means, time- and money-weighted, real returns). Expect short data stems and options that differ by one classic slip.

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Checked against SIDC Module 12 Study Outline (Jul–Dec 2026) Topic 5; Brealey, Myers and Allen, Principles of Corporate Finance; Bodie, Kane and Marcus, Investments; CFA Institute Level I, Rates and Returns. Calculations verified in Python. As at October 2026. Independent prep, not endorsed by SIDC or the SC.

Must-know for the exam

NPV = Σ CFt ÷ (1 + r)^t − initial outlay; accept independent projects with NPV > 0 at the cost of capital.
IRR is the rate where NPV = 0; accept if IRR > cost of capital, but rank mutually exclusive projects by NPV.
Profitability index = PV of inflows ÷ initial outlay; above 1 means positive NPV.
Simple payback ignores discounting and all cash after the cut-off; discounted payback fixes only the first flaw.
Effective annual rate = (1 + nominal ÷ m)^m − 1: 12% monthly gives 12.68%.
Expected return = Σ probability × return; variance = Σ probability × (return − expected)².
Coefficient of variation = standard deviation ÷ mean: lower is less risk per unit of return.
Geometric mean ≤ arithmetic mean; use the geometric mean for compound growth of wealth.
Time-weighted return removes clients' cash flows (judges the manager); money-weighted is the IRR of the investor's flows.
Real return: (1 + nominal) ÷ (1 + inflation) − 1; 8% nominal at 3% inflation is 4.85%.

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Traps that cost marks

Adding up undiscounted cash flows, or quoting the PV of inflows as the NPV.
Accepting any project with a positive IRR. The hurdle is the cost of capital, not zero.
Rounding to whole years instead of interpolating within the payback year.
Reporting the simple payback when the question asks for the discounted one.
Inverting the ratio. PI puts the PV of inflows on top.
Ranking mutually exclusive projects by IRR or payback instead of NPV.
Using the firm's borrowing rate as the discount rate for a risky project.
Using the annuity-due factor when payments come at the end of each year.

Time value of money

Discount future cash at the opportunity cost of capital, the return forgone on investments of equal risk. PV = FV ÷ (1 + r)^n; an ordinary annuity is worth C × [1 − (1 + r)^−n] ÷ r; a perpetuity C ÷ r.

Case	Formula	Example
Lump sum PV	FV ÷ (1 + r)^n	RM100,000 in 3 years at 8% = RM79,383
Annuity PV	C × [1 − (1 + r)^−n] ÷ r	RM10,000 × 5 years at 6% = RM42,124
Perpetuity	C ÷ r	RM5,000 at 8% = RM62,500
Effective rate	(1 + i ÷ m)^m − 1	12% monthly = 12.68%

Trap: using simple interest, or the annuity-due factor for end-of-year payments.

Takeaway: compound forward, discount back, and match the payment timing to the formula.

Capital budgeting rules

NPV adds the discounted cash flows, outlay included. IRR is the discount rate at which NPV is zero. The profitability index divides the PV of inflows by the outlay. Payback counts years to recover the outlay. Only incremental cash flows count: include opportunity costs and working capital, exclude sunk costs and unchanged overhead allocations. Discount nominal cash flows at a nominal rate.

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