The Future Value of Both Annuities
Annuities are a succession of fixed payments an individual or a business is required to pay over a particular time frame. As stated by Cleaves, Hobbs & Noble (2013), usually, these payments are made quarterly, semiannually, annually, monthly, or weekly.
The FV of an ordinary annuity:
Periods = 5*4 = 20
Period interest rate (semi-annual) = 8%/4 = 2%
TV = 24.297
FV = annuity payment*TV
FV = $2,500*24.297 = $60,742.50
The future value of the annuity due:
FV = annuity* table value (1+ period interest)
FV = $2,500 (24.297)*(1.08)
FV = $65,601.90
Based on the calculations, ordinary annuity is lower than annuity due. Generally, with ordinary annuities, payments are done at the close of the specific time frame, while with annuity due payments are done immediately, or at the start of a covered period instead of at the end. Because in annuity due payments are made sooner than an ordinary annuity, the PV of an annuity due is generally higher than an ordinary annuity. As interest rates increase an ordinary annuity’s value reduces, and vice versa ( Cleaves, Hobbs & Noble, 2013) . Therefore, the best annuity option is the annuity due option, as the interest accumulated is one more period compared to the ordinary annuity, although they have similar number of payments.
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The Sinking Fund Payment
A sinking fund is created by an individual or entity for a certain goal at a future date. The sinking fund is calculated as follows:
Cost of the machine = $45,000
Useful life Period = 3 years
Bi-annual rate = 12%
Thus, there will be 6 semi-annual periods and a 6% interest rate period.
The compound table value = 0.1433626
Sinking fund = 45,000 *0.1433626 = $6,451.32
Comparison
Based on the calculations made above for the annuity due and sinking fund, a comparison can be made regarding the shorter period and greater rate of interest for the two. Essentially, for annuity due, the shorter the period, the higher the interest, while for sinking fund, the longer the period, the higher the interest.
Prioritization Plan
The company needs to ensure that the purchases decisions are made wisely, since the absence of the machine will stop the production process, as well as the profitability in the long run. Therefore, the replacement of the machine is vital to the business and it should be does quickly to prevent the loss of profits. Thus, the first option of purchases would the best, because it would mean making higher payments while getting the maximum returns.
Reference
Cleaves, C., Hobbs, M., & Noble, J. (2013). Business Math Brief: Pearson New International Edition . Pearson Higher Ed.
