Business Finance • TVM, Valuation, Capital Budgeting & Cost of Capital – Comprehensive Notes

Time Value of Money (TVM)

• Definition: A ringgit/dollar received today is worth more than the same amount in the future because it can be invested and earn a return.
  • Delayed investment ⇒ lost opportunity.
  • Underpins virtually every decision in finance (savings, investment, valuation, capital budgeting).

Core TVM Terminology

• Present Value (PV): What a future cash flow is worth today.
• Future Value (FV): What a cash flow received today will grow to in the future.
• Discounting: Process of moving future cash flows back to present ($PV$).
• Compounding: Process of moving cash flows forward in time ($FV$).
• Mathematical link
  $FV = PV(1+i)^{n}$
  $PV = FV \times \bigg[\frac{1}{(1+i)^{n}}\bigg]$
  where $i$ = periodic interest/discount rate; $n$ = number of compounding periods.

Compounding & Future Value

• Simple annual compounding
  • Example: Deposit $500$ at $5\%$ p.a.
  • $FV_{2} = 500(1.05)^{2} = 551.25$
  • $FV_{5} = 500(1.05)^{5} = 638.14$
  • Tabular build-up shows interest-on-interest (power of compounding).
• Graphical insight
  • Investing $100$ @ $8\%$ p.a. ⇒ $FV<em>{10}=215.89$, $FV</em>{15}=317.22$.
  • Higher rate dramatically enlarges future sums (e.g., $100$ @ $20\%$ for $30$ yrs ⇒ $23{,}737.63$).

Non-Annual Compounding

• If interest is compounded $m$ times a year:
  $FV = PV\Big(1 + \frac{i_{APR}}{m}\Big)^{n\times m}$
• More frequent compounding ⇒ higher $FV$.
  • Deposit $50{,}000$ @ $10\%$ APR compounded monthly for $10$ yrs
    $FV = 50{,}000 \big(1+\frac{0.10}{12}\big)^{120}=135{,}352.07$
    vs annual compounding $FV=129{,}687.12$.
• Limiting case – continuous compounding (not explicitly examined in slides, but conceptually)
  $FV = PV\,e^{i n}$.

Discounting & Present Value

• Key question: “What is the value today of a future cash flow?”
  • Use the Present Value Interest Factor (PVIF):
    $PVIF = \frac{1}{(1+i)^{n}}$
    $PV = FV \times PVIF$.
• Example: PV of $100{,}000$ receivable in 25 yrs @ $5\%$
  $PV = 100{,}000\big[\frac{1}{1.05^{25}}\big]=29{,}530$.

Solving for Unknown n or i

• Rearrange $FV=PV(1+i)^{n}$.
• Example (solve $n$): $10{,}000 → 200{,}000$ @ $15\%$ ⇒ between 21-22 yrs.
• Example (solve $i$): $50{,}000 → 1{,}000{,}000$ in 30 yrs ⇒ required $i≈10–11\%$.

Annuities

Ordinary Annuity (payments at end of period)

• Future value:
  $FV_{n}=PMT\bigg[\frac{(1+i)^{n}-1}{i}\bigg]$.
• Example: Deposit $3{,}000$ each year for 10 yrs @ $5\%$ ⇒ $FV=37{,}740$.
• Solving for PMT: $PMT=\frac{FV_{n}\,i}{(1+i)^{n}-1}$
  • To reach $100{,}000$ in 18 yrs @ $12\%$ ⇒ $PMT=1{,}793.73$.
• Solving for i or n uses FVIFA tables / financial calculator.

Present value of ordinary annuity

$PV = PMT\bigg[\frac{1-(1+i)^{-n}}{i}\bigg]$.

• PV of $10{,}000$ for 10 yrs @ $10\%$ ⇒ $PV=61{,}445$.

Annuity Due (payments at beginning)

• $FV<em>{AD}=FV</em>{OA}(1+i)$
• $PV<em>{AD}=PV</em>{OA}(1+i)$ (because each cash flow is 1 period earlier).

Bond Valuation & Corporate Debt

Corporate Borrowing Choices

• Private debt: loans from financial institutions & private placements.
  • Advantages: speed, lower flotation cost, flexibility.
  • Disadvantages: higher interest, restrictive covenants, later SEC issues.
• Public debt: Bonds underwritten & sold by investment banks.

Basic Bond Features

• Indenture, par value (usually $1{,}000$), coupon rate, maturity, asset claims, call & conversion provisions.
• Bond valuation = PV of coupons (ordinary annuity) + PV of par.
  $P = \sum_{t=1}^{n}\frac{C}{(1+YTM)^{t}} + \frac{FV}{(1+YTM)^{n}}$.
• Example: MOZEK 8% coupon, 12 yrs, YTM 12% ⇒ $P=752.23$.
• Relationship summary:
  1. Price inversely related to market YTM.
  2. Premium if $YTM < coupon$, discount if $YTM > coupon$.
  3. Price converges to par as maturity approaches.
  4. Longer maturity ⇒ greater interest-rate risk.

Types of Corporate Bonds

• Debentures (unsecured), subordinated debentures, mortgage bonds (secured), Eurobonds, zero-coupon/very-low coupon, junk (high-yield), floating-rate, convertible bonds.

Stock Valuation

Common Stock (infinite life, residual claim)

• Constant-growth Dividend Discount Model (DDM):
  $P<em>0=\frac{D</em>1}{k<em>{cs}-g}$ where $D</em>1=D_0(1+g)$.
• Example: $D_0=6$, $g=5\%$, $k=12\%$ ⇒ $P=90$.

Preferred Stock (perpetuity)

• $P<em>{ps}=\frac{D</em>{ps}}{k_{ps}}$.
  • Example: $D=12$, $k=8\%$ ⇒ $P=150$.

Investment Decision Criteria (Capital Budgeting)

Net Present Value (NPV)

• $NPV = -CF<em>0 + \sum</em>{t=1}^{n}\frac{CF_t}{(1+k)^{t}}$.
• Accept if NPV>0 (adds shareholder wealth).
• Example: Saber Electronics project $NPV=+573{,}817$ ⇒ accept.

Profitability Index (PI)

• $PI=\frac{PV\;of\;future\;CF}{|CF_0|}$.
• Accept if PI>1. Example PNG Pharma $PI=1.0733$.

Internal Rate of Return (IRR)

• Discount rate that makes $NPV=0$.
• Accept if IRR > required\;return.
• May conflict with NPV for mutually exclusive projects or non-normal CFs.

Payback & Discounted Payback

• Payback = years to recover initial outlay (ignores TVM & CF beyond cutoff).
• Discounted Payback uses PV CFs; still ignores post-payback CFs.

Popularity (survey)

• CFOs commonly use NPV & IRR; payback remains widely used for its simplicity.

Cost of Capital & Weighted Average Cost of Capital (WACC)

Purpose

• Represents the minimum required return on new investments to satisfy all capital providers.
• Used to:
  • Value the entire firm.
  • Serve as starting discount rate for projects.
  • Benchmark managerial performance.

Component Costs

1. Cost of Debt ($k_d$): Market YTM on existing/new debt.
   • After-tax cost $k_d(1-T)$ because interest is tax-deductible.
   • Approximate YTM shortcut
     $YTM \approx \frac{C+\frac{FV-PV}{t}}{\frac{FV+PV}{2}}$.
     Example: Par $1{,}000$, coupon $5\%$, price $900$, $t=10$ ⇒ $YTM≈6.32\%$; after-tax (30%) $4.42\%$.
2. Cost of Preferred ($k<em>{ps}$):
   $k</em>{ps}=\frac{D<em>{ps}}{P</em>{ps}}$ (dividend/price).
3. Cost of Equity ($k_{cs}$):
   • Dividend Growth (DCF) approach: $k<em>{cs}=\frac{D</em>1}{P_0}+g$.
   • Alternately CAPM (not detailed in slides): $k<em>{cs}=R</em>f+\beta(R<em>m-R</em>f)$.

WACC Formula

$\text{WACC}=w<em>d\,k</em>d(1-T)+w<em>{ps}\,k</em>{ps}+w<em>{cs}\,k</em>{cs}$

• Weights ($w$) based on market values of each capital component.
• Example: Templeton original structure
  • $w<em>d=0.25$, $w</em>{ps}=0.125$, $w_{cs}=0.625$.
  • $k<em>d(1-T)=6\%$, $k</em>{ps}=10\%$, $k_{cs}=15\%$.
  • $WACC=0.25(0.06)+0.125(0.10)+0.625(0.15)=12.125\%$.
• Revised structure (37.5% debt, no preferred) ⇒ $WACC=11.625\%$ (cheaper because low-cost debt replaces higher-cost capital).

Factors Affecting WACC

• Risk profile of the firm (affects required returns).
• Capital structure (mix of debt vs equity).
• Tax rate (impacts after-tax debt cost).
• Market conditions (interest rates, equity risk premiums).

Quick Reference: Corporate Bond Ratings

• Investment Grade:
  • Prime $Aaa/AAA$; High Grade $AA$; Upper-Medium $A$; Medium $BBB$.
• Non-Investment (Speculative): $BB, B, CCC, CC, C, D$ (default).

Ethical / Practical Implications & Connections

• TVM underlies ethical allocation of capital—delaying returns carries opportunity cost.
• Capital budgeting discipline (NPV, IRR) ensures resources deployed to projects that increase stakeholder wealth.
• Mis-estimating WACC can lead to under-investment (too high) or wealth destruction (too low).
• Bond rating agencies’ assessments affect cost of debt and signal firm risk to the market.

Essential Formula Sheet (LaTeX Ready)

• $FV = PV(1+i)^{n}$
• $PV = FV(1+i)^{-n}$
• $FV_{n}=PMT\big[\tfrac{(1+i)^{n}-1}{i}\big]$
• $PV_{n}=PMT\big[\tfrac{1-(1+i)^{-n}}{i}\big]$
• $P<em>{bond}=\sum</em>{t=1}^{n}\frac{C}{(1+YTM)^{t}}+\frac{FV}{(1+YTM)^{n}}$
• $P<em>{cs}=\frac{D</em>1}{k_{cs}-g}$
• $P<em>{ps}=\frac{D</em>{ps}}{k_{ps}}$
• $k<em>{cs}=\frac{D</em>1}{P_0}+g$
• $k<em>{ps}=\frac{D</em>{ps}}{P_{ps}}$
• $k_{d,after}=YTM(1-T)$
• $WACC=w<em>d k</em>d(1-T)+w<em>{ps}k</em>{ps}+w<em>{cs}k</em>{cs}$