# Essays on AFM231 Financial Mathematics Math Problem

Question One. In making a decision on which of the projects I will invest in, I will calculate the present value of the value of the cash flows then less the cost (Ross, 2006). However, in this case there is no need to less initial cost because the three projects have the same costs. Calculation of net present valueXPROJECT I- PERTHYEAR12345\$\$\$\$\$CASH FLOWS300000500000500000600000600000PVIF 5%n 0.9524 0.9070 0.8638 0.8227 0.7835 present value 285,714.29 453,514.74 431,918.80 493,621.48 470,115.70 Net present value 2,134,885.01 PROJECT TWO-ROCKHAMPTONYEAR 12345\$\$\$\$\$cash flows580000480000480000480000480000PVIF 5% 0.9524 0.9070 0.8638 0.8227 0.7835 Present values 552,380.95 435,374.15 414,642.05 394,897.19 376,092.56 Net present cash flows 2,173,386.90 PROJECT THREE-ADELAIDEYEAR12345\$\$\$\$\$cash flows450000450000500000500000620000PVIF 5% 0.9524 0.9070 0.8638 0.8227 0.7835 Present values 428,571.43 408,163.27 431,918.80 411,351.24 485,786.22 Net present cash flows 2,165,790.95 From the calculation of the net present values, the project with the highest returns is project two-Rockhampton.

This project should be chosen because the benefits in terms of the level of returns among the three projects will be the highest.

One advantage about the cash flows in project two is that they are constant. If the discount rate changes to 4%The results of the cash flows when using 4% illustrate that the project with the highest level of returns will still be project two. In the case, the projects were being discount by 7%. The calculation of net present value would resultXPROJECT I- PERTHYEAR12345\$\$\$\$\$CASH FLOWS300000500000500000600000600000PVIF 5%n0.93460.87340.81630.76290.7130present value 280,373.83 436,719.36 408,148.94 457,737.13 427,791.71 Net present value 2,010,770.97 PROJECT TWO-ROCKHAMPTONYEAR 12345\$\$\$\$\$cash flows580000480000480000480000480000PVIF 5%0.93460.87340.81630.76290.7130Present values 542,056.07 419,250.59 391,822.98 366,189.70 342,233.37 Net present cash flows 2,061,552.71 PROJECT THREE-ADELAIDEYEAR12345\$\$\$\$\$cash flows450000450000500000500000620000PVIF 5%0.93460.87340.81630.76290.7130Present values 420,560.75 393,047.43 408,148.94 381,447.61 442,051.43 Net present cash flows 2,045,256.15 A change to 7% does not change the project to be selected, project two still has the highest level of Net present cash flows and thus will have the highest returns. Graphical illustration of the effects of changes in interest ratesProject one-PERTHProject two- ROCKHAMPTONProject three-ADELAIDEQuestion TwoThe Difference between Discounting and CompoundingDiscounting is a process of looking at the future payments or a series of income and calculating the value of such future payments to today’s value/ present value.

This is possible given a discount rate/ rate of return of the incomes. The future payments may be different in nature; some of the cash flows will be the equal while others will be different. Some will be earned at the end of the year while others will be earned at the beginning of the year (Buchanan, 2006). In case the future payments do not have a fixed time period and occur in perpetuity the Gordon formula 5will be used in discounting.

This formula calculates the present value in perpetuity of the ending year’s cash flows. The present value calculated in then discounted using the given discount rate. The present value in Gordon formula= PV= NCF (1+g)/ (k-g)CompoundingCompounding is used in respect to the interest rates. Compounding involves the calculation of different forms of returns or cash flows. In the calculation, of interest in the first period involves the calculation multiplication of the interest with the principal amount. However, the second and other periods the amount of interest is calculated by multiplying the interest rate by the principal amount and interest values of the previous periods (Cartledge, 2000). An annuity is a series of returns/ incomes/ payments/ cash flows through a time period.

The uniqueness of these cash flows is that they equal for in all the periods. The annuities can be classified into ordinary annuity and annuity due Ordinary annuity, results from the occurrence of cash flows at the end of the of the give years. We calculate the ordinary annuity value at present and in the future.