Finance

Corporate Finance Fundamentals

Time value of money, NPV, and WACC — the core valuation toolkit.

A cash flow $C$ received in $t$ years is worth $P V = \frac{C}{( 1 + r ) ^{t}}$ today, where $r$ is the discount rate. A project's net present value is $N P V = - C_{0} + \sum_{t = 1}^{n} \frac{C _{t}}{( 1 + r ) ^{t}}$ ; accept if $N P V > 0$ .

1. Present value
easy
You will receive $\$ 10{,}000 $in$ 3 $y e a r s . I f t h e ann u a l d i sco u n t r a t e i s$ 8%$, what is its present value?
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$PV = \dfrac{10{,}000}{(1.08)^3} = \dfrac{10{,}000}{1.259712} \approx \$ 7{,}938$.

The $\$ 10{,}000 $f u t u r e p a y m e n t i s w or t hab o u t$ $7{,}938 $t o d a y a t an$ 8%$ opportunity cost.
2. Net present value
medium
A project costs $\$ 1{,}000 $t o d a y an d r e t u r n s$ $600 $a tt h ee n d o f y e a r 1 an d$ $700 $a tt h ee n d o f y e a r 2. A t a d i sco u n t r a t eo f$ 10%$, should you accept it?
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$P V_{1} = \frac{600}{1.10} = 545.45$ ; $P V_{2} = \frac{700}{1.1 0 ^{2}} = \frac{700}{1.21} = 578.51$ .

$NPV = -1000 + 545.45 + 578.51 = \$ 123.96 > 0$.

Since $N P V > 0$ , accept the project — it adds about $\$ 124 $o f v a l u e a t a$ 10%$ required return.
3. WACC
hard
A firm is financed $60%$ by equity (cost $12%$ ) and $40%$ by debt (cost $6%$ before tax). The corporate tax rate is $25%$ . Compute the weighted average cost of capital.
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$W A C C = w_{E} r_{E} + w_{D} r_{D} (1 - T)$ .

After-tax cost of debt: $6% \times (1 - 0.25) = 4.5%$ .

$W A C C = 0.60 \times 12% + 0.40 \times 4.5% = 7.2% + 1.8% = 9.0%$ .

The tax shield on interest lowers the effective cost of debt, pulling the WACC below the simple weighted average of the two gross rates.

Corporate Finance Fundamentals

1. Present value

2. Net present value

3. WACC

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