Valuation Techniques

Question 1

Explain Compounding

Answer 1

Calculating a future value of a present payment

Question 2

Explain Discounting

Answer 2

Calculating present value of a future payment

Question 3

Explain Internal Rate of Return

Answer 3

Yield to maturity. Annual rate of growth that an investment is expected to generate.

Question 4

Compounding formula

Answer 4

V (t = n) = A0 * (1 + r)^n

Question 5

Discounting formula

Answer 5

A0 = Vn / (1 + r)^n

where 1 / (1+r)^n is the discount factor

Question 6

Compounding frequencies rates formulas

Answer 6

Simple: payment * (1+r)
Half yearly: payment * (1+r/2)^2
Quarterly: payment * (1+r/4)^4
Monthly: payment * (1+r/12)^12
Daily: payment * (1+r/365)^365
Continuous: payment * e^r

Question 7

Effective Annual Rate

Answer 7

(1 + Re) = (1 + R / m) ^m

for continuous
Rcont.comp. = e^R - 1
and
R = ln (1 + Rcont.comp.)

Question 8

Formula to go from compounding rate to simple rate

Answer 8

R = m((1+Rcomp)^(1/m) - 1)

Question 9

Discounted Present Value (DPV) formula

Answer 9

DPV = V1/ (1+r) + V2/ (1+r)^2 + …

Question 10

Net Present Value (NPV) formula

Answer 10

NPV = DPV - Cost

Question 11

How to find IRR

Answer 11

Rate r needed to make NPV = 0

NPV = DPV - Cost = 0
then solve for the unknown factor r

Question 12

How do NPV and IRR relate to each other

Answer 12

NPV and IRR give the same investment decision for independent projects with “normal cash flows” (= investment followed by returns)

For cash flows that change from negative/positive more than once, IRR gives multiple solutions and can’t be used so use NPV

–> For mutually exclusive projects use NPV

Question 13

Enterprise DCF

Answer 13

V (whole firm) = DPV (FCF’s to equity and bondholders)

where FCF = Operating cash flows - gross physical investment

Question 14

Value of Equity

Answer 14

V (equity) = V (whole firm) - V (debt outstanding)

Question 15

Fair value of a share

Answer 15

= V (equity) / N

where N = number of shares outstanding

Question 16

Discounted Present Value Model

Answer 16

DPV = CF1 / (1+k) + CF2 / (1+k)^2 + …

Question 17

Discount Rate

Answer 17

k
Quantifies the riskiness / uncertainty of future dividends

= interest rate + risk premium

Question 18

Continuing Value

Answer 18

The present value at a future point in time (!!) of all future cash flows when we expect stable growth rate forever

CV (at t = n) = FCFn*(1+g)/(k-g)

when g = 0 –> CV (at t = n) = FCFn/k

Question 19

Choose discount rate for unlevered firm (no debt)

Answer 19

Assume the historically observed return on equity correctly reflects the payment for risk that shareholders require from this company/project

Use the average return on equity for this firm/project as discount rate

Question 20

Choose discount rate for levered firm (combination of debt and equity financing)

Answer 20

Assume debt-equity ratio will remain broadly unchanged after new project is completed

Use weighted average cost of capital

WACC = (1-z)Rs + zRb (1-t)

z = B/V = proportion of debt
(1-z) = S/V
V = market value of the firm = S + B

S = market value of outstanding equity ( N * stock price)
B = market value of outstanding debt (bonds and bank loans)
Rs = average return on equity in industry
Rb= interest rate on bonds
t = corporate tax rate

Question 21

Economic Profits

Answer 21

EP = (ROC - WACC) * Capital Stock K

Question 22

Economic Value Added

Answer 22

= Profit - Capital Charge
= Profit - WACC * ‘Adjusted Capital’ K

Question 23

Present Value of the firm using EP or EVA

Answer 23

= net capital stock at t=0 + DPV (of EP or EVA using WACC as discount rate)