MIT 15.401 - Finance Theory I: Capital Budgeting & Asset Pricing Flashcards

Question 1

Net Present Value (NPV)

Accepted Answer

The difference between the present value of cash inflows and the present value of cash outflows over time.

$$	ext{NPV} = \sum_{t=1}^T \frac{C_t}{(1+r)^t} - C_0$$

Where $C_t$ is cash flow at time $t$, $r$ is the discount rate, and $C_0$ is initial investment. **Rule:** Accept projects with $	ext{NPV} > 0$.

Question 2

Internal Rate of Return (IRR)

Accepted Answer

The discount rate $r^*$ that equates the present value of future cash flows to the initial investment, setting the NPV to zero:

$$	ext{NPV} = \sum_{t=1}^T \frac{C_t}{(1+r^*)^t} - C_0 = 0$$

**Rule:** Accept a project if its $	ext{IRR} > 	ext{Cost of Capital}$.

Question 3

Pitfalls of the IRR Decision Rule

Accepted Answer

1. **Multiple IRRs:** Cash flows with sign changes can yield multiple rates.
2. **Mutually Exclusive Projects:** IRR ignores scale (a 100% return on $1 is worse than a 20% return on $1,000).
3. **Reinvestment Rate Assumption:** Assumes cash flows are reinvested at the IRR rather than the cost of capital.

Question 4

Present Value of a Perpetuity

Accepted Answer

A constant cash flow $C$ received forever starting in period 1:

$$	ext{PV} = \frac{C}{r}$$

For a **growing perpetuity** with growth rate $g$ ($r > g$):

$$	ext{PV} = \frac{C_1}{r - g}$$

Question 5

Present Value of an Annuity

Accepted Answer

A stream of equal cash flows $C$ occurring at equal intervals for $T$ periods:

$$	ext{PV} = \frac{C}{r} \left[ 1 - \frac{1}{(1+r)^T} ight]$$

Question 6

Bond Pricing Equation

Accepted Answer

The price of a bond paying periodic coupon payments $C$ and face value $F$ at maturity $T$:

$$P = \sum_{t=1}^T \frac{C}{(1+y)^t} + \frac{F}{(1+y)^T}$$

Where $y$ is the Yield to Maturity (YTM).

Question 7

Yield to Maturity (YTM)

Accepted Answer

The total rate of return anticipated on a bond if it is held until maturity. It represents the Internal Rate of Return (IRR) of the bond's cash flows, equating market price to the present value of coupon and principal cash flows.

Question 8

Bond Price-Yield Relationship

Accepted Answer

Bond prices and yields have an **inverse relationship**: * If $y > ext{Coupon Rate} \implies ext{Bond sells at a Discount} (P < F)$. * If $y < ext{Coupon Rate} \implies ext{Bond sells at a Premium} (P > F)$. The price-yield curve is **convex**.

Question 9

Macaulay Duration

Accepted Answer

The weighted average maturity of a bond's cash flows, measuring price sensitivity to yield changes:

$$D = \sum_{t=1}^T t \cdot \frac{\frac{C_t}{(1+y)^t}}{P}$$

**Modified Duration** measures percentage price change per change in yield: $D_{mod} = \frac{D}{1+y}$.

Question 10

Expected Return of a Portfolio

Accepted Answer

The weighted sum of the expected returns of individual assets in the portfolio:

$$E(R_p) = \sum_{i=1}^N w_i E(R_i)$$

Where $w_i$ is the weight of asset $i$ and $\sum w_i = 1$.

Question 11

Variance of a 2-Asset Portfolio

Accepted Answer

Measures total portfolio risk:

$$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 	ext{Cov}(R_1, R_2)$$

Or using correlation $ho_{12}$:
$$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 ho_{12}$$

Question 12

Principle of Portfolio Diversification

Accepted Answer

Combining assets with correlation $\rho < 1$ reduces portfolio variance without sacrificing expected return. As the number of assets $N$ increases, idiosyncratic (unsystematic) risk approaches zero, leaving only market (systematic) risk.

Question 13

Systematic vs. Unsystematic Risk

Accepted Answer

* **Systematic (Market) Risk:** Macroeconomic factors affecting all assets. Cannot be diversified away. Measured by Beta ($
\beta$).
* **Unsystematic (Idiosyncratic) Risk:** Firm-specific risks that can be eliminated through diversification.

Question 14

Beta ($\beta$)

Accepted Answer

A measure of an asset's systematic risk relative to the market portfolio:

$$\beta_i = \frac{	ext{Cov}(R_i, R_m)}{	ext{Var}(R_m)}$$

* $\beta = 1$: Moves in lockstep with market.
* $\beta > 1$: More volatile than market.

Question 15

Capital Asset Pricing Model (CAPM)

Accepted Answer

Relates expected return of an asset to its systematic risk relative to the market:

$$E(R_i) = R_f + \beta_i \left( E(R_m) - R_f \right)$$

Where $R_f$ is the risk-free rate and $E(R_m) - R_f$ is the Market Risk Premium (MRP).

Question 16

Security Market Line (SML)

Accepted Answer

A graphical representation of CAPM plotting Beta (x-axis) against Expected Return (y-axis).
* Intercept = Risk-free rate ($R_f$).
* Slope = Market Risk Premium ($E(R_m) - R_f$).
* Assets above the SML are **undervalued** (positive Alpha); assets below are **overvalued**.

Question 17

Sharpe Ratio

Accepted Answer

Measures total risk-adjusted return (reward per unit of total risk):

$$	ext{Sharpe Ratio} = \frac{E(R_p) - R_f}{\sigma_p}$$

The slope of the Capital Allocation Line (CAL).

Question 18

Weighted Average Cost of Capital (WACC)

Accepted Answer

The overall required rate of return for a company financed by debt and equity:

$$	ext{WACC} = \frac{E}{V} r_e + \frac{D}{V} r_d (1 - 	au_c)$$

Where $E$ = equity, $D$ = debt, $V = E + D$, $r_e$ = cost of equity, $r_d$ = cost of debt, and $	au_c$ = corporate tax rate.

Question 19

Modigliani-Miller Theorem (Proposition I - No Taxes)

Accepted Answer

In frictionless capital markets (no taxes, no bankruptcy costs, perfect information), the total market value of a firm is independent of its capital structure:

$$V_L = V_U$$

Leverage affects how cash flows are split between debt and equity, but not total market value.

Question 20

Modigliani-Miller Theorem (Proposition I - With Taxes)

Accepted Answer

Because interest payments on debt are tax-deductible, corporate borrowing creates an interest tax shield:

$$V_L = V_U + 	ext{PV(Tax Shield)} = V_U + 	au_c D$$

Question 21

Efficient Market Hypothesis (EMH)

Accepted Answer

Asset prices fully reflect all available information:
1. **Weak Form:** Prices reflect all historical trading data/prices.
2. **Semi-Strong Form:** Prices reflect all publicly available information.
3. **Strong Form:** Prices reflect all public and private (insider) information.

MIT 15.401 - Finance Theory I: Capital Budgeting & Asset Pricing

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