1 WIUU BBA RM Sensitivity Sensitivity. Tornado chart.

1 WIUU BBA RM Sensitivity Sensitivity. Tornado chart. DOL. DFL. DTL. Study materials: Slides RWJ: Ch 8.3. BM: Ch 10.1.

2 Sensitivity Analysis - The study of how variations of outcome are due to changes in variables. It is used to see how a dependent variable reacts to changes in an independent variable. A method of predicting how changes in a particular factor will change the outcome. Usually performed by creating a range of change for an independent variable and predicting an outcome range. (SMA 2A) “The effect of a change in a variable (such as sales) on the risk or profitability of an investment.” (Barron’s Dictionary of Finance and Investment Terms) Sensitivity

3 Beta as indicator of market risk Modified Duration (MD) RRR in Capital budgeting analysis; NPV profile NB: The higher the value of a sensitivity factor, the higher (some particular, type of) risk. Sensitivity: cases in Finance

4 Sensitivity in Finance: Beta

5 Sensitivity in Finance: MD Modified Duration measures the responsiveness of a bond’s price to interest rate changes. Measured in times. MD = D / (1 + YTM/[no. of C]) Example: Duration: 4.373 Yr, YTM: 8%. MD – ? Solution: MD = 4.373 / (1 + 0.08/[1]) = 4.049 (times)

6 Change in price of a bond is dependent on the bond’s MD and the change of market interest rate for similar instruments: P% = - MD * r% Sensitivity in Finance: MD

7 Example: MD = 4.049, r% = 0.5%, P0 = $960.07. P%, P$, P1 - ? Solution: P% = -4.049 * 0.5% = -2.02%; P$ = $960.07 * -2.02% = ($19.39) P1 = P0 * (1 + r%) = P0 + P$ = $940.68 Sensitivity in Finance: MD

8 CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n + . . . + + - CFi NPV = Sensitivity in Finance: Capital Budgeting

9 If the “hurdle rate” is 13%, then: $10,000 $7,000 $10,000 $12,000 $15,000 (1.13)1 (1.13)2 (1.13)3 + + + - $40,000 (1.13)4 (1.13)5 NPV = + = - $1,428 Sensitivity in Finance: Capital Budgeting

10 RRR, “Hurdle rate”, % 0 3 6 9 12 15 IRR = 11.47% NPV at r = 13% Total expected Cash flows for years 1 thru 5 NPV, $ $K 15 10 5 0 -4 «NPV profile of the Project» -1,428 Sensitivity in Finance: Capital Budgeting

11 Example: +/- 1% in each variable will result in changes in NI

12 Sensitivity: Tornado Chart

13 Tornado Chart: Exercise Prepare 2 tornado charts (2009 vs. 2008) of changes in profit. Explain in which year the bank’s RM is more effective. Build up a risk map. Include downside risks only. Estimate different probabilities for the 4 currencies. Source: “Finbank”, Annual Report of 2009.

14 A leverage indicator summarizing the effect that a particular amount of the operating leverage has on a company's operating profit. Operating leverage involves using a large proportion of fixed costs to variable costs in the operations of a company. The higher the DOL, the more sensitive the EBIT relative to a change in sales revenue, all other factors remaining the same. Unlike the common D/A, D/E, and EM ratios, the DOL needs TWO PERIODS (P&L) data. DOL = ∆% EBIT / ∆% Revenue Degree of Operating Leverage

15 DOL (times) = ∆% EBIT / ∆% Revenue The higher DOL, the higher the business risk. Degree of Operating Leverage, DOL

16 DOL and BEP are interconnected: Using the contribution margin approach, find: FC = $15,500 VC(u) = $8 BEP(u) = ? BEP($) = ? DOL and BEP

17 The “concept” formula of the DOL that underlies the general formula given below: Degree of Operating Leverage NB: DOL is found using P&L data (2 periods). “Classic” financial leverage is found using B/S data (1 date).

18 DFL (times) = ∆% NI / ∆% EBIT DFL is not the same as the Financial leverage ratio (A/E), though both are of the same nature. DFL = ? Degree of Financial Leverage, DFL

19 DTL = DOL * DFL = ∆% NI / ∆% Revenue The higher DTL, the higher the business risk. DTL = ? NB: DTL usually has positive correlation with beta. Degree of Total Leverage, DTL Also: Degree of Combined Leverage

20 Practice: find DOL, DFL, DTL for the 2 companies