Part - 1

The present value “Present Value = P_{0} = P_{n} / (1+I)^{n” }is a representation of the reciprocal o compound interest obtained from the product of the present value factors and the future values ( Engel & West,, 2004). In consideration, the forthcoming price is reduced to the extant value. For instance, in a case where a bank account is worth $ 15000 in one year at a discounted rate of 7%, the present value for the bank account today would be the product of the present value factors and the future value. In this case, the future value is $ 15000, while the present value factors would be obtained from the table of value factors for the period of one year at the interest rate of 7%, which is 0.9346. This gives $ 14019 as the present value obtainable from the product of $15000 and 0.9346. On the contrary, if the discounted rate is only 4%, the present value would be obtained from the product of the future value, which is $ 15000 and the present value factor from the present value tables, which is 0.965. This gives $ 14422.50 as the present value, which is higher than the previous discounted rate of 7%. This is due to the fact that the reciprocal of the compound interest is inversely proportional to the discounted rates ( Adedeji, 2001).

In another case, in which there are two bank accounts A and B such that account A will worth $ 6,500 in one year while account B will be worth $ 12,600 in two years bearing in mind that the discounted rate for both accounts is 6%, then the present value for each of these accounts would be obtained through synthesizing the product of their individual future values and the present value factors ( Cunningham, Nikolai,, Bazley, Kavanagh, Slaughter, & Simmons, 2011). For instance, for account A, the present value is obtained through multiplying $ 6500 as the future value with 0.9434 from the factor tables, which gives $ 6132.1. On the other hand, the present value for bank account B would be obtained through synthesizing the product of $ 12600 as the future value and 0.8900. This gives $ 11214 as the present value for account B.

In another scenario in which one inherits a gold mine that is expected to bring about gold deposits worthy $49,000,000 in the first year, $61,000,000 in the second year and $85,000,000 for the third year, then the computation of the present values at a discounting rate of 7% would involve a representation of the whole stream. For the first year, the present value is calculated by multiplying the future value, which is $49,000,000 by the present value factor at the discounting rate of 7%, which is 0.9346. This gives a present value of $45795400. In the second year, the future value is $61000000, which is multiplied by the present factor value at a discounting rate of 7%, which is equal to 0.8734 ( Cunningham, Nikolai,, Bazley, Kavanagh, Slaughter, & Simmons, 2011). This gives a present value of $53277400. Additionally, the present value for the third year is calculated through finding the product of $85,000,000 and 0.8163, which are the future value and the present value factors at a discounting rate of 7%. This gives a present value of $69385500. Computing the total present value involves summation of all the three present values obtained in the above synthesis. This implies that the total amount payable is a summation of $69385500, $53277400 and $45795400. This gives $168458300 as the total amount that the inheritor of the gold mine pays right now in order to receive the three payments in the future ( Engel & West,, 2004).

The present value obtained at a discount rate of 5% involves multiplying the present value factors with the respective future values. In the first year, the present value would be the product of $49000000 and 0.9524, which gives $46667600. In the second year, the present value is obtained through multiplying $61000000 with 0.9070, which gives $55327000. Additionally, the present value for the third year would be obtained through multiplying $85000000 with 0.8638, which gives $73423000 as the present value. This shows that the total present value for the three years at a discounting rate of 5% is $175417600. Moreover, operating at a discounting rate of 3% gives a total present value of $47574100 for the first year, which is a product of $49000000 and 0.9709, $57462000 for the second year as a product of $61000000 and 0.9426 and $777835 as a product of $85000000 and 0.9151. The total amount payable at this discounting rate of 3% is the summation of the three present values, which gives $182819600. This brings about a conclusive evidence that the present values are inversely proportional to the discounting rate in the sense that the higher the discounting rate, the lower the present value, while the converse is also true that the higher the discounting rate, the lower the discounting rate ( Adedeji, 2001).

Part - 2

The “Real Estate Brokerage Business Plan”, whose baseline of formation depends on the sponsorship of “RJ Wagner and Assoc. Realty” forms one of the business projects that should have the highest risk factors from the point of view of the investors (Masters, 2006). Moreover, this project would be evaluated using the highest discounting rate because they have a requirement of lower net present values. The other two business projects with the same requirement of high risk factors are the “Truck Stop Business Plan” and the “Shaved Ice Beverage Business Plan.” These business projects also require evaluation of the net present values using the highest discounting rates since they lie in low net present value margins. Conversely, the “Shaved Ice Beverage Business Plan” would have the lowest discounting rates since it bears the lowest risk factors as compared to the other two. The major risk factor in this business plan is the fluctuation in weather conditions that is adjustable through use of refrigeration as a source of limiting the risk factor of poor weather conditions (Godby, & Vahey, 2012).

The possible risk factors for the “Real Estate Brokerage Business Plan” lies in the requirements that the corporation has to finance the payments of brokers for the viability of its business plan. This forms a setback as it is a source of the increased cost of production. This also puts the corporation at the highest probability of evaluation of its net present values using the highest discounting rates as a form of reducing the influence of the acquired net present value. This is from the fact that the higher the discounting rate, the lower the net present value. Moreover, the “Truck Stop Business Plan” has a major risk of sourcing for the products, which are mainly gas and fuel (Wagner, Tiffany, & Peterson, 2010). By consideration, these products have the highest risk factors in terms of fluctuation of commodity prices.

Fluctuation in commodity prices has an impact on the general profitability of the organization in relation to the projections of the business plan. This puts the organization at the requirement that the evaluation of the net present value using the highest discounting rates in order to reduce the amount payable as the advancement towards the net present value. This shows that the higher the risk factors, the higher the requirement of evaluation of the net present value using the higher discounting rates to obtain lower net present values advanced to each business project or plan (Wagner, Tiffany, & Peterson, 2010).