Module 3 TVM and WACC

Financial Primer: Time Value of Money and WACC

Introduction: Learning Objectives

• Overview of key topics including Time Value of Money and Weighted Average Cost of Capital (WACC).

• Focus on understanding and practical calculation of:

  • Time Value of Money (TVM) - defining future value and present value.

  • WACC - understanding cost of capital, cost of debt, cost of equity, and calculating WACC.

Time Value of Money (TVM)

• The concept of Time Value of Money indicates that money has different values at different times due to potential earning capacity.

• Factors that influence TVM calculations:

  • Amount of cash flows.

  • Appropriate interest rate.

  • Timing of cash flows (the point in time when cash flow is expected).

Future Value (FV)

• Definition: The future value is the amount of money that an investment made today will grow to over a period of time at a given interest rate.

• Formula:
  $FV = PV imes (1 + i)^n$
  where:

  • FV = Future Value

  • PV = Present Value

  • i = Periodic interest rate

  • n = Number of periods

• Example: What is the future value of $100 invested for 2 years at 10% per year compounded annually?

  • Calculation:
    $FV = 100 imes (1 + 0.10)^2$
    $FV = 100 imes 1.21 = 121$

Practice Problems on Future Value

• Problem 1: If Penny Blossom invests $5000 today at 5% compounded annually, what will it amount to in 5 years?

  • Options:

  • A) $6,000

  • B) $6,250

  • C) $6,381.41

  • D) $6,500

• Problem 2: TICO Corporation's current dividend of $5 per share grows by 4% annually. What will the dividend amount be after 8 years?

  • Options:

  • A) $7.00

  • B) $6.84

  • C) $5.60

  • D) $7.20

Present Value (PV)

• Definition: The present value calculates how much a future sum of money is worth today, assuming a specific interest rate.

• Formula:
  $PV = rac{FV}{(1 + i)^n}$
  where:

  • PV = Present Value

  • FV = Future Value

  • i = Periodic interest rate

  • n = Number of periods

• Example: What is the present value of $2,382 to be received after 3 years at a discount rate of 6%?

  • Calculation:
    $PV = rac{2382}{(1 + 0.06)^3}$
    $PV ext{(using calculations)} = 2382 / 1.191 = 2000$

Practice Problems on Present Value

• Problem 1: A department store offers two payment options for $10,000 today or $12,000 in 3 years at an 8% discount rate. Which option should Penny Blossom choose?

  • Options:

  • A) Option A: $10,000 today

  • B) Option B: $12,000 in 3 years

  • C) Equal Value

  • D) Insufficient information

• Problem 2: Sarah wishes to buy a luxury sedan priced at $68,500 in 2 years with a 9% annual interest rate. How much must be invested today?

  • Options:

  • A) $57,655

  • B) $64,230

  • C) $52,890

  • D) $59,775

Present Value of a Stream of Payments

• Example: Annual cash flows of $200, $400, $600 over three years with a 12% discount rate.

• Calculation for PV: $PV = rac{200}{(1 + 0.12)^1} + rac{400}{(1 + 0.12)^2} + rac{600}{(1 + 0.12)^3}$

  • Detailed breakdown results in:

  • Year 1: $178.57

  • Year 2: $318.88

  • Year 3: $427.08

  • Total PV = $924.53

Practice Problems on Streams of Payments

• Problem: Penny Blossom considers a machine that will yield returns of $200, $400, $600, and $800 over 4 years at a 12% annual return rate. What is the maximum expenditure for this machine?

Cost of Capital

• Definition: The cost of capital encompasses the total costs associated with permanent sources of capital like long-term debt, preferred stock, and common equity.

• Key Points:

  • Costs are calculated on an after-tax basis.

  • Only debt costs need adjustments since equity costs are already computed after taxes.

  • Understanding WACC is crucial as it encompasses all sources of capital.

Cost of Debt

• Definition: The relevant cost is the after-tax yield to maturity (YTM).

• Example: YTM includes the return investors expect from bonds issued by the firm.

• After-tax cost formula: $R<em>d = R</em>{bt} imes (1 - T)$ where:

  • $R_d$ = After-tax cost of debt

  • $R_{bt}$ = Before-tax yield to maturity

  • $T$ = Tax rate

Practice Problems on Cost of Debt

• Problem: Penny Blossom's existing bonds have a YTM of 7.5% and a marginal tax rate of 30%. What is the after-tax cost of debt?

  • Options:

  • A) 5.25%

  • B) 7.50%

  • C) 4.75%

  • D) 6.15%

Cost of Common Equity

• CAPM Formula:
  $R<em>E = R</em>{RF} + \beta imes (R<em>M - R</em>{RF})$

• Example Calculation: Assuming a risk-free rate of 4%, market return of 10%, and a Beta of 1.2:
  $R_E = 0.04 + (0.10 - 0.04) imes 1.2 = 0.112 ext{ or } 11.2$

Practice Problems on Cost of Common Equity

• Problem: If Penny Blossom's stock has a Beta of 1.35, risk-free rate of 1.5%, and market risk premium of 6.5%, what is its cost of equity?

  • Options:

  • A) 9.75%

  • B) 10.28%

  • C) 8.00%

  • D) 7.25%

Weighted Average Cost of Capital (WACC)

• Definition: WACC is a critical calculation used to determine a firm’s cost of capital weighted by the proportion of equity and debt.

• Formula:
  $WACC = W<em>d imes (1 - T) + W</em>e$
  where:

  • $W_d$ = Weight of Debt

  • $W_e$ = Weight of Equity

• Example Calculation: Assuming 1/3 financing from debt and 2/3 from equity at respective costs:
  WACC = rac{1}{3}(0.05)(1 - 0.3) + rac{2}{3}(0.112) = 8.64 ext{%}

Practice Problems on WACC

• Problem: Calculate WACC for Penny Blossom with:

  • Cost of equity = 10.28%

  • After-tax cost of debt = 5.25%

  • % Debt = 40%, % Equity = 60%

  • Options:

  • A) 8.27%

  • B) 7.52%

  • C) 9.15%

  • D) 6.84%

Session Wrap-up

• Summary of learned topics on the time value of money, cost of capital, and WACC calculation, with relevant practice problems for application.