Chapter 13:

Just to get the ball rolling, I am providing the step by step calculations for figure 13.1. Using my calculations as a guide, you need to show the step by step calculations, for parts I, II and III, for figure 13.2.

Part I: Project without the Growth Option:

NPV (Good): You can use row 2 of the calculator with the following inputs:

CF0 = -3000; C01 = 1500; F01 = 3; I = 12; CPT NPV; NPV = $603

Note: If you don't feel comfortable using the frequency key, you can enter the cash flows as follows:

CF0 = -3000; C01 = 1500; F01 = 1; C02 = 1500; F02 = 1; C03 = 1500; F03 =1

You follow the same procedure for the bad outcome and you get NPV = -$358

Expected NPV:

(.5*603) + (.5*(-358)) = $122

Standard Deviation:

SQRT[..5(603-122)^2 + .5(-358-122)^2] = $480

CV:

480/122 = 3.93

Part II: Project with the Option

The calculations are identical to part I. When you follow the calculations noted above, you get the following numbers:

Expected NPV = $1,503

Std. Dev. = $1,861

CV = 1.24

Part III: Value of the Option

Value of the option is the expected NPV with the option - expected NPV without the option. In this case:

Value of the option = $1,503 - $122 = $1,381

Notes:

1. If expected NPV without the option is negative, the project would not be accepted and so the option has no value.

2. Although the concepts in the four figures are fundamentally different, the calculations are identical.

Chapter 13 Real Options and Other Topics in Capital Budgeting 461 Part I. Project Without the Timing Option B FIGURE 13.3 Analysis of a Timing Option (dollars in thousands) A D G H 5 6 7 8 Prob 50% 50% NPV@ 12% $1,804 -$1,919 -$58 $1,861 -32.23 TO 11 13 16 77 18 19 20 Outcome Cash Flow at End of Period 0 Good 2 -$3,000 Bad $2.000 $2,000 $2,000 -$3,000 $450 $450 $450 Expected NPVI Standard Deviation (0) Coefficient of Variation - CVO / Expected NPV Part Il. Delry the Decision Until We Know the Market Conditions Dutcome Cash Flow at End of Period Prob. 0 1 2 Good 50% $0 -$3,000 $2,000 $2,000 Bad 50% SO $0 $0 $0 Expected NPV Standard Deviation (a) Coefficient of Variation = CV= / Expected NPVI 21 Part III. Value of the Option 22 Expected NPV with the timing option 23 Expected NPV without the timing option 24 25 CASE 1: If the expected NPV without the timing option is positive, then Expected NPV with the Expected NPV without Value of the Option = timing option the timing option NPV 12% $339 $0 $170 $170 1.00 $170 -$58 NA 27 28 CASE 2: If the expected NPV without the timing option is negative, then Value of the Option = Expected NPV with the 0 timing option $170 29 30 Note: If a negative NPV project does not have a timing option, then it would not be undertaken. In these cases, the expected NPV without the timing option is zero. 31 32 33 VALUE OF OPTION = $170 34 Note: Under the Delay situation, we must find the NPV as of t = 0. If we set the cash flow for t=0 at SO, then using a calculator or Excel, we automatically find the NPV at t = 0. However, if we let CF, =-3000, CF = 2000, N = 2, and I/YR = 12, we get an NPV = $380 under the Good outcome and an expected NPV of $190. Note, though, that these NPVs are as oft = 1, so we must discount them back year at 12% to achieve comparability with the NPV calculated for not delaying the project and arrive 35 at the correct answer. nditi will need and realize an NPV of $339,000, while and thus will have Chapter 13 Real Options and Other Topics in Capital Budgeting 461 Part I. Project Without the Timing Option B FIGURE 13.3 Analysis of a Timing Option (dollars in thousands) A D G H 5 6 7 8 Prob 50% 50% NPV@ 12% $1,804 -$1,919 -$58 $1,861 -32.23 TO 11 13 16 77 18 19 20 Outcome Cash Flow at End of Period 0 Good 2 -$3,000 Bad $2.000 $2,000 $2,000 -$3,000 $450 $450 $450 Expected NPVI Standard Deviation (0) Coefficient of Variation - CVO / Expected NPV Part Il. Delry the Decision Until We Know the Market Conditions Dutcome Cash Flow at End of Period Prob. 0 1 2 Good 50% $0 -$3,000 $2,000 $2,000 Bad 50% SO $0 $0 $0 Expected NPV Standard Deviation (a) Coefficient of Variation = CV= / Expected NPVI 21 Part III. Value of the Option 22 Expected NPV with the timing option 23 Expected NPV without the timing option 24 25 CASE 1: If the expected NPV without the timing option is positive, then Expected NPV with the Expected NPV without Value of the Option = timing option the timing option NPV 12% $339 $0 $170 $170 1.00 $170 -$58 NA 27 28 CASE 2: If the expected NPV without the timing option is negative, then Value of the Option = Expected NPV with the 0 timing option $170 29 30 Note: If a negative NPV project does not have a timing option, then it would not be undertaken. In these cases, the expected NPV without the timing option is zero. 31 32 33 VALUE OF OPTION = $170 34 Note: Under the Delay situation, we must find the NPV as of t = 0. If we set the cash flow for t=0 at SO, then using a calculator or Excel, we automatically find the NPV at t = 0. However, if we let CF, =-3000, CF = 2000, N = 2, and I/YR = 12, we get an NPV = $380 under the Good outcome and an expected NPV of $190. Note, though, that these NPVs are as oft = 1, so we must discount them back year at 12% to achieve comparability with the NPV calculated for not delaying the project and arrive 35 at the correct answer. nditi will need and realize an NPV of $339,000, while and thus will have