CAIIB Paper 3 Module B Quiz 10

An NPV profile shows how a project’s net present value changes as the discount rate changes. It can help compare projects and identify the IRR where the NPV curve crosses zero.

When cash-flow signs change multiple times, the NPV equation may have more than one root, producing multiple IRRs. NPV at the required return is more reliable in such cases.

The traditional IRR interpretation assumes interim cash flows can be reinvested at the IRR, which may be unrealistic when IRR is very high. NPV assumes reinvestment at the cost of capital, often more plausible.

MIRR typically discounts negative cash flows to present value and compounds positive cash flows at a specified reinvestment rate, then computes a single return measure. It can reduce some IRR limitations.

Cash flows and discount rates must be expressed consistently in nominal or real terms. Inconsistent inflation treatment can distort the present value estimate.

In a standard unlevered NPV approach, project cash flows are calculated before financing costs and discounted at WACC. Including interest in cash flows as well can double-count financing effects.

Using the Fisher relationship, real rate = (1.08/1.03) − 1 ≈ 4.85%. The simple approximation 8% − 3% = 5% is close but not exact.

Earlier cash flows have a higher present value at a positive discount rate, all else equal. They may also provide liquidity and reinvestment opportunities sooner.

An annuity due pays at the beginning of each period, so each payment is discounted for one fewer period than an ordinary annuity. Its present value is therefore higher when the discount rate is positive.

Present value of a level perpetuity = annual payment ÷ discount rate = ₹2 lakh ÷ 0.10 = ₹20 lakh, assuming the first payment arrives one year from now and continues indefinitely.

The growing perpetuity formula TV = CF1/(r−g) requires the discount rate r to exceed perpetual growth g. If g is equal to or above r, the formula is not economically valid.

IRR is a percentage return and can favour small projects. NPV measures absolute value created and is generally preferred when choosing between mutually exclusive investments.

Net working capital investment = increase in current operating assets − increase in spontaneous operating liabilities = ₹3 lakh − ₹1 lakh = ₹2 lakh cash outflow.

Sunk costs are past expenditures that are unrecoverable and unaffected by the current decision. Including them can distort the comparison of future alternatives.

The abandonment decision compares the present value of continuing cash flows with the value available from exit, including salvage proceeds and closure costs. Historical cost is generally sunk.

Portfolio-like project risk depends on covariance. Imperfect or negative correlation can diversify fluctuations, so aggregate risk is not simply the sum of standalone risks.

Portfolio beta is the market-value weighted average of component betas. With equal weights, beta = 0.5×0.5 + 0.5×1.5 = 1.0.

Expected portfolio return = 0.40×8% + 0.60×12% = 3.2% + 7.2% = 10.4%. This weighted average does not by itself measure portfolio risk.

A discount rate that is too low for a project’s risk produces a present value that is too high, all else equal. Project-specific risk should be reflected consistently in the cash flows or discount rate.

Investment choices determine funding needs and expected returns; financing affects risk and cost of capital; dividend policy affects retained funds and investor distributions. Coordinating them supports sustainable value creation.