Overall, there is a large difference between NPVs of the two projects while there is a smaller difference between their IRRs. Hence, Project ‘p’ should be selected over Project ‘q’.
Moreover, IRR ranking is misleading here because the base investment (initial cash outflow) in the two projects is not the same. The cash outflow in Project ‘p’ ($200) is twice that of project ‘q’ ($100). Hence, it would not be appropriate to compare the two projects on IRR basis.
2. Let ‘S’ be the periodic saving, ‘i’ be the interest rate, ‘P’ be the annual payments to be ensured, ‘n’ be the number of years for which savings are done and ‘N’ be the number of years for which payments are to be ensured. According to the given data,
S has to be calculated
Now, Future value of all savings at the end of 65 years= Present Value of all payments at the end of 65 years
i.e. S[(1+i)^n-1]/i = P (1-(1/(1+i)^N))/i
i.e. S[(1+.04)^20-1]/.04 = 30000 (1-(1/(1+.04)^15))/.04
i.e. S= $11,201.25
Hence, the annual savings must be $11,201.
3. Table 3.1 depicts the Interest paid, Principal Paid and Principal Balance at the end of first 10 years. Here, Interest paid is calculated as 10% of principal balance in the previous year. The Principal paid is calculated as the difference of Yearly Installment and Interest
Table 3.1: Yearly Installment Plan at 10% rate of interest throughout
Year Interest paid Principal paid Principal balance
0 0 0 200000
The yearly installment can be calculated by using formula for Present value or ‘pmt’ function in excel. It comes out as $21,215. The principal balance at the end of 1 year comes out as $198,784 and at the end of 10 years as $180,622. If mortgage rates drop to 8%, the yearly installments after 4th year are calculated using principal balance at the end of 4th year. This comes out as $17,979. Table 3.2 depicts Table 3.2: Yearly Installment Plan at 10% rate of interest till 4th year and 8% thereafter Year Interest paid Principal paid Principal balance 0 0 0 200000 1 20000 1,215.85 198784.1503 2 19878.41503 1,337.43 197446.7157 3 19744.67157 1,471.18 195975.5377 4 19597.55377 1,618.30 194357.2418 5 15548.57934 2,430.85 191926.3911 6 15354.11129 2,625.32 189301.0724 7 15144.08579 2,835.34 186465.7282 8 14917.25826 3,062.17 183403.5565 9 14672.28452 3,307.15 180096.411 these changes. Now, if $3000 is paid to refinance this change, the value of Net Present Value of cash outflow at the end of 4th year is given by the sum of Future value of installments up till 4th year at 10%, Present value of installments from 4th year to 9th year at 8% and $ 3000. This is equal to $173,249. If $ 3000 is not paid and rather invested in CD at 6% return, the value of Net Present Value of cash outflow at the end of 4th year is given by [Future value of installments up till 4th year at 10% + Present value of installments from 4th year to 9th year at 10% - $ 3000[(1.06)^5-1]. This is equal to $177,872. Hence, refinancing the mortgage is a better option as the NPV of net cash outflows is lower. It is assumed here that after the 9th year, the house is sold or the returns from it are similar in both options. 4. The efficiency of the compensation plan is dependent upon the expected revenue of