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Capital Budget Decision Model - NPV & PI in Financial Mathematics

Understanding the net present value (NPV) and profitability index (PI) in capital budgeting decisions is crucial. NPV helps in assessing the profitability of an investment by comparing the present value of cash inflows with outflows. Long-term decisions in finance involve significant costs and implications, different from short-term choices like daily meal options. Calculating NPV for project cash flows like Project A, B, and C aids in selecting the most lucrative investment opportunity.

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Capital Budget Decision Model - NPV & PI in Financial Mathematics

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  1. Commercial Subjects Group Level 3 Subject Financial Mathematics 2 – (Fin 316/806) Chapter Unit 3 Capital Budget Decision Model – NPV & PI Title Second Semester ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023 ) ينهمو ينف ( ثلاثلا ديحوت ) – ( ىوتسملا اثلا ثل - ةيوناثلا ةلحرملا

  2. Learning Objectives Learning Objectives At this unit, our students will learn: INITIATION ACTIVITY ► The calculation of the net present value. OBJECTIVE 1 ► The calculation of the profitability index. OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  3. INATIATION ACTIVITY INATIATION ACTIVITY What is the meaning of net present value? How to use it in your capital budget decision? INITIATION ACTIVITY The capital budgeting decision model that uses all the discounted cash flows of a project is net present value (NPV), one of the single most important models in finance. The NPV of an investment is the present value of all benefits (cash in-flows) minus the present value of all costs (cash outflow) of the project. If the net amount is positive (benefits exceed costs), the project or choice is a “go” (accept). If the net amount is negative (costs exceed benefits), the project or choice is a “no-go” (not- accept). If two projects are being compared, the one with the highest positive net present value is selected. OBJECTIVE 1 OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  4. The calculation of the net present value What is the difference between a short-term decision and long-term decision? INITIATION ACTIVITY A short-term decision, you will decide today what to eat for your next meal. This decision may involve a set of choice with varying costs. The choice affects you for only a short period, and the difference in cost of the different menu options is relatively small. In addition, you will face the next meal selection. OBJECTIVE 1 OBJECTIVE 2 Then there are long-term decisions, recall for a moment your decision concerning which college to attend. This decision affects you for a number of years and carries with it significant financial costs. Moreover, this choice may well have been a once-in-a-lifetime decision. Although you can change schools after your initial choice, you cannot pick a different school to attend every few hours as you can with your menu choice at mealtime. FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  5. The calculation of the net present value Example 3-3-1: ► Given the cash flow of three projects A, B and C, and using the net present value decision model, which projects do you accept and which project you will choose ? INITIATION ACTIVITY Cash Flow Cost (Cash Outflow) Cash inflow year 1 Cash inflow year 2 Cash inflow year 3 Cash inflow year 4 Cash inflow year 5 Project A BD10,000 BD3,500 BD3,500 BD3,500 BD3,500 BD3,500 Project B BD10,000 BD2,000 BD3,400 BD4,000 BD5,000 BD6,000 Project C BD10,000 BD5,500 BD4,500 BD4,000 BD3,000 BD2,000 OBJECTIVE 1 OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  6. The calculation of the net present value Answer: Answer: 1. Project A: ( Fixed Cash Inflow): Cash Flow (CF) -10,000 3,500 3,500 3,500 3,500 3,500 × (? + ?)−? Year PV of Cash flow INITIATION ACTIVITY × (1 + 6%)0= 1 × (1 + 6%)−1= 0.9434 × (1 + 6%)−2= 0.8900 × (1 + 6%)−3= 0.8396 × (1 + 6%)−4= 0.7921 × (1 + 6%)−5= 0.7473 0 1 2 3 4 5 -10,000 3,301.9 3,115 2,938.6 2,772.35 2,615.55 4,743.4 OBJECTIVE 1 Net Present Value (NPV) OR: Other Answer: OR: Other Answer: OBJECTIVE 2 ???= PMT × PVIF n ,r = 3,500 ×4.21236 ~ 4.2124 =BD14,743.4 NPV= 14,743.4 FINAL EVALUATION – 10,000 = BD4,743.4 FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  7. The calculation of the net present value 2. Project B: ( Changeable Cash Inflow): (? + ?)−?CF Cash Flow (CF) INITIATION ACTIVITY × (? + ?)−? Year PV of Cash flow × (1 + 6%)0 × (1 + 6%)−1= 0.9434 × (1 + 6%)−2= 0.8900 × (1 + 6%)−3= 0.8396 PV 0 -10,000 = 1 -10,000 OBJECTIVE 1 1 2,000 1,886.8 2 3,400 3,026 358.4 OBJECTIVE 2 3 , 3 4,000 × (1 + 6%)−4= 0.7921 960.5 3 , 4 5,000 FINAL EVALUATION × (1 + 6%)−5= 0.7473 483.8 4 , 6 , 5 6,000 715.5 Net Present Value (NPV) FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  8. The calculation of the net present value 2. Project C: ( Changeable Cash Inflow): Cash Flow (CF) -10000 5,500 4,500 4,000 3,000 2,000 Net Present Value (NPV) × (? + ?)−? Year PV of Cash flow INITIATION ACTIVITY × (1 + 6%)0= 1 × (1 + 6%)−1= 0.9434 × (1 + 6%)−2= 0.8900 × (1 + 6%)−3= 0.8396 × (1 + 6%)−4= 0.7921 × (1 + 6%)−5= 0.7473 0 1 2 3 4 5 -10,000 188.7 005 358.4 376.3 494.6 423 5 , 4 , 3 , 2 , 1 , 6 , (? + ?)−?CF OBJECTIVE 1 PV OBJECTIVE 2 FINAL EVALUATION ► We accepted all three projects by using NPV method. The best we choose is project B because it has the highest NPV. FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  9. The calculation of the net present value Advantages and Disadvantages of NPV Method: Advantages and Disadvantages of NPV Method: INITIATION ACTIVITY  Advantages: Advantages: 1- It considers the time value of money. 2- Helpful in decision-making. OBJECTIVE 1  Disadvantages: Disadvantages: 1- The calculation of the required rate of return does not have set guidelines. 2- Projects may be incomparable because of different investment terms and sizes. 3- Hidden costs are not considered. OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  10. The calculation of profitability index Example 3-3-1: ► Given the cash flow of three projects A, B and C, and using profitability index decision model, which projects do you accept and which project you will choose ? INITIATION ACTIVITY Cash Flow Cost (Cash Outflow) Cash inflow year 1 Cash inflow year 2 Cash inflow year 3 Cash inflow year 4 Cash inflow year 5 Project A BD10,000 BD3,500 BD3,500 BD3,500 BD3,500 BD3,500 Project B BD10,000 BD2,000 BD3,400 BD4,000 BD5,000 BD6,000 Project C BD10,000 BD5,500 BD4,500 BD4,000 BD3,000 BD2,000 OBJECTIVE 1 OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  11. The calculation of profitability index ► The profitability index (PI) is a modification of the NPV to produce the ratio of the present value of the benefits (future cash inflow) to the present value of the costs (initial investment): INITIATION ACTIVITY Profitability Index = ??????? ????? ?? ???????? ??????? ????? ?? ????? Profitability Index = ???+???? OBJECTIVE 1 ???? Profitability Index = 1 +??? ???? OBJECTIVE 2 ► The decision criterion is very straightforward: if PI > 1, accept the project; if PI < 1reject the project. Thus, when the PI is greater than 1, the benefits exceed the costs. FINAL EVALUATION ► If you already have the NPV of a project and it has a standard cash flow setup of all cash outflow at the beginning and cash inflow at a later period, you can quickly calculate the PI of the project. FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  12. The calculation of profitability index Answer: PI project A = 4,743.4+10,000 = 1.47434 > 1 (Accept) INITIATION ACTIVITY 10,000 PI project A = 6,715.5+1,0000 = 1.67155 > 1 (Accept) OBJECTIVE 1 10,000 PI project A = 6,423+1,0000 = 1.6423 > 1 (Accept) OBJECTIVE 2 10,000 ► We accepted all three projects by using PI method .The best we choose is project B because it has the highest PI. FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  13. The calculation of profitability index Advantages and Disadvantages of PI Method: Advantages and Disadvantages of PI Method:  Advantages: Advantages: 1. PI considers the time value of money. 2. PI considers analysis of all cash flows of entire life. 3. PI makes the right in the case of different amount of cash outlay of different project. 4. PI ascertains the exact rate of return of the project.  Disadvantages: Disadvantages: 1. It is difficult to understand the interest rate or discount rate. 2. It is difficult to calculate profitability index if two projects have different useful life. INITIATION ACTIVITY OBJECTIVE 1 OBJECTIVE 2 FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  14. EVALUATION Exercises ( Exercises (3 3- -1 1): ): The following three projects” their cash flow and using 8% discount rate. Project A Project B Project C Cash Flow BD BD BD INITIATION ACTIVITY Cost (Initial Investment) 20,000 20,000 20,000 Cash flow year 1 6,000 8,000 3,000 OBJECTIVE 1 Cash flow year 2 6,000 7,500 4,000 Cash flow year 3 6,000 6,000 5,000 OBJECTIVE 2 Cash flow year 4 6,000 5,000 6,000 REQUIRED: REQUIRED: Which projects do you accept and which projects do you reject by using: a. Net Present Value Method. b. Profitability Index Method. FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  15. The calculation of the net present value Answer: Answer: 1. Project A: ( Fixed Cash Inflow): Cash Flow (CF) -20,000 × (? + ?)−? Year PV of Cash flow INITIATION ACTIVITY × (1 + 8%)0= 1 × (1 + 8%)−1= 0.9259 × (1 + 8%)−2= 0.8573 × (1 + 8%)−3= 0.7938 × (1 + 8%)−4= 0.7350 0 -20,000 1 5555.4 6,000 2 5143.8 6,000 OBJECTIVE 1 3 4762.8 6,000 4 4410 -128 6,000 Net Present Value (NPV) OR: Other Answer: OR: Other Answer: OBJECTIVE 2 ???= PMT × PVIF n ,r FINAL EVALUATION = 6,000 ×3.3120 = BD19872 NPV= 20000 – 19872 = BD128 FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  16. The calculation of the net present value Answer: Answer: 2. Project B: Cash Flow (CF) × (? + ?)−? Year PV of Cash flow INITIATION ACTIVITY × (1 + 8%)0= 1 0 -20,000 -20,000 × (1 + 8%)−1= 0.9259 1 7407.2 8,000 OBJECTIVE 1 × (1 + 8%)−2= 0.8573 2 6429.75 7,500 × (1 + 8%)−3= 0.7938 3 4762.8 6,000 OBJECTIVE 2 (? + ?)−?CF × (1 + 8%)−4= 0.7350 4 3675 5,000 Net Present Value (NPV) 2274.75 FINAL EVALUATION PV FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  17. The calculation of the net present value Answer: Answer: 3. Project C: Cash Flow (CF) -20,000 × (? + ?)−? Year PV of Cash flow INITIATION ACTIVITY × (1 + 8%)0= 1 × (1 + 8%)−1= 0.9259 × (1 + 8%)−2= 0.8573 × (1 + 8%)−3= 0.7938 × (1 + 8%)−4= 0.7350 Net Present Value (NPV) 0 -20,000 1 2777.7 3,000 OBJECTIVE 1 2 3429.2 4,000 (? + ?)−?CF 3 3969 5,000 OBJECTIVE 2 4 4410 -5414.1 6,000 PV FINAL EVALUATION ► We accepted project B by using NPV method and reject projects A&C .We rejected projects A&C because NPV had negative value. FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  18. The calculation of profitability index Answer: PI project A = −128+20,000 = 0.9936 < less than 1 (Reject) INITIATION ACTIVITY 20,000 PI project A = 2274.75+2,0000 = 1.1137 > 1 (Accept) OBJECTIVE 1 20,000 PI project A = −5414.1+2,0000 = 0.7293 < less than 1 (Reject) OBJECTIVE 2 20,000 ► We accepted all three projects by using PI method .The best we choose is project B because it has the highest PI. FINAL EVALUATION FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

  19. END OF LESSON Thanks FIN 316/806 UNIT 3 CAPITAL BUDGET DECISION MODEL ميلعتلاو ةيبرتلا ةرازو – م 2024 - ي ساردلا ماعلا 2023

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