Question

5. Growth options Aa Aa Companies often come across projects that have positive NPV opportunities in which the company does not invest. Companies must evaluate the value of the option to invest in a new project that would potentially contribute to the growth of the firm. These options are referred to as growth options Consider the case of Mitata Co.: Mitata Co. is considering a three-year project that will require an initial investment of $45,000. It has estimated that the annual cash flows for the project under good conditions will be $40,000 and $11,000 under bad conditions. The firm believes that there is a 60% chance of good conditions and a 40% chance of bad conditions. If the firm is using a weighted average cost of capital of 13%, the expected net present value (NPV) of the project is Mitata Co. wants to take a potential growth option into account when calculating the project's expected NPV. If conditions are good, the firm will be able to invest $2,000 in year 2 to generate an additional cash flow of $15,000 in year 3. If conditions are bad, the firm will not make any further investments in the project. Using the information from the preceding problem, the expected NPV of this project-when taking the growth option into account-is Mitata Co.'s growth option is worth

Answer 1

Part 1:

• Step 1 is to calculate the NPV under good and bad scenarios:

  • NPV Calculation
    Year	Remark	0	1	2	3
    CF	Good Scenario		40000	40000	40000
    Initial outlay		-45000
    Discount factor formula	at 13%	1/1.13^0	1/1.13^1	1/1.13^2	1/1.13^3
    Discount factor		1	0.884955752	0.783146683	0.693050162
    PV	Discount factor x CF	-45000	35398.23009	31325.86733	27722.00649
    NPV	Sum of all PV	49446.10391
    NPV Calculation
    Year	Remark	0	1	2	3
    CF	Bad Scenario		11000	11000	11000
    Initial outlay		-45000
    Discount factor formula	at 13%	1/1.13^0	1/1.13^1	1/1.13^2	1/1.13^3
    Discount factor		1	0.884955752	0.783146683	0.693050162
    PV	Discount factor x CF	-45000	9734.513274	8614.613517	7623.551785
    NPV	Sum of all PV	-19027.32142

• Next step is to find probability weighted NPV:
  • 
    Probability weighted NPV = ProbabilityGod×NPVGoortProbabilitybad× N PViad
    
  • 
    Probability weighted NPV0.60 x 49446.10391 +0.40 x -19027.32142
    
  • 
    Probability weighted NPV = $22056.73
    

Part 2: We now incorporate the growth option into NPV calculation:

Year	Remark	0	1	2	3
CF	Good Scenario		40000	40000	40000
Initial outlay		-45000
Additional investment				-2000
Additional CF					15000
Total CF	CF+Initial outlay+Additional investment+Additional CF	-45000	40000	38000	55000
Discount factor formula	at 13%	1/1.13^0	1/1.13^1	1/1.13^2	1/1.13^3
Discount factor		1	0.884955752	0.783146683	0.693050162
PV	Discount factor x CF	-45000	35398.23009	29759.57397	38117.75893
NPV	Sum of all PV	58275.56298
NPV Calculation
Year	Remark	0	1	2	3
CF	Bad Scenario		11000	11000	11000
Initial outlay		-45000
Discount factor formula	at 13%	1/1.13^0	1/1.13^1	1/1.13^2	1/1.13^3
Discount factor		1	0.884955752	0.783146683	0.693050162
PV	Discount factor x CF	-45000	9734.513274	8614.613517	7623.551785
NPV	Sum of all PV	-19027.32142

• Next step is to find probability weighted NPV:
  • 
    Probability weighted NPV = ProbabilityGod×NPVGoortProbabilitybad× N PViad
    
  • 
    Probability weighted NPV0.60 x 58275.56298 +0.40 x -19027.32142
    
  • 
    Probability weighted NPV = $27354.41
    

Value of growth option = NPV with growth option -NPV without growth option

Value of growth option = 27354.40922-22056.73378

Value of growth option = $5297.68