present value of your bank account

Part I:

  1. Suppose your bank account will be worth $7,000.00 in one year.  The interest rate (discount rate) that the bank pays is 8%.  What is the present value of your bank account today?  What would the present value of the account be if the discount rate were only 3%?

PV = ∑j=1 ((FV/ (1+μ) j)

  1. =7,000/1.08


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  1. = 7,000/1.03

= $6796.12

  1. Suppose you have two bank accounts, one called Account A and another Account B.  Account A will be worth $4,000.00 in one year.  Account B will be worth $9,600.00 in two years.  Both accounts earn 5% interest.  What is the present value of each of these accounts?

PV = ∑ j=1 ((FV/ (1+μ) j)

Account A

= 4000/1.051

= $3809.52

Account B

= 9,600/1.052

= $8707.48

  1. Suppose you just inherited a gold mine.  This gold mine is believed to have three years worth of gold deposit.  Here is how much income this gold mine is projected to bring you each year for the next three years:

Year 1: $42,000,000

Year 2: $62,000,000

Year 3: $99,000,000

PV = ∑ j=1 ((FV/ (1+μ) j)

At 8%

= (42,000,000/ 1.081) + (62,000,000/ 1.082) + (99,000,000/1.083)

= $170,633,287.6

At 6%

(42,000,000/ 1.061) + (62,000,000/ 1.062) + (99,000,000/1.063)

= $177,924,729.8

At 4%

(42,000,000/ 1.041) + (62,000,000/ 1.042) + (99,000,000/1.043)

= $185,717,740.1

The computations indicate that the present value of the gold mine increases as the rate of discount reduces. Therefore, if the discount rate is low, the amount that needs to be invested now to guarantee the same future value of income must be higher (Pierson 2008).

 Part IIBusiness Risk

Business risk is generally assessed on five levels. First, the risk is assessed with respect to the product offered or proposed for operation of the venture. Secondly, the investor would be interested in knowing the amount of market risk that the business venture is likely to face. Such risks include a decline in the growth of a business venture, misinterpretation of the size or the growth of the market due to limited knowledge and misallocation of resources due to an unrealistic market study. These risks make the risk of uncertainty even greater and hence an investor may not be ready to put funds where there is not full information or knowledge of the mentioned factors (Hiles 2002).

The third risk that an investor may want to look at when assessing the proposed venture is the business risk. The investor is interested in investing in a great business. Although a business venture might be observed to involve a new technology or production of a great product, the investor is actually interested in the viability of the whole business in the market since new technologies do not translate to outright business success. Lastly, it is important for the financier to assess the financial risk involved (Pratt et al 2000). A business that seems to generate very little revenue while involves heavy outlay may not attract an investor.

In addition to the above method of assessing the risk in the proposed venture, the prospective may find it important to look at the venture in terms of an industry analysis. By looking at the industry risk analysis, the financier will look at the competitor risk and look at the strategies put in place to cope with this risk. A business venture formulated with a background idea that it is going to operate in a vacuum without competition is not worth financing. The ability of the competitors should not be underestimated.

In an environment with high technological revolution, it is likely that a business will face a threat from disruptive technologies. Therefore, the financier will assess whether the business faces a potential threat from technology transition risks brought by the disruptive technologies. Such technologies are also likely to increase the level of competition by creating loopholes for new market entrants.

Presence of substitute products in the market offers a good reason to the financier to believe that the substitute risk will have a negative impact on the survival and profitability of the proposed venture. If the products to be produced or sold have substitutes in the market and they are fairly priced as compared to what the venture can price, then this only implies that the proposed business is to be based on speculation (Pierson 2008). However, the rule of the thumb is that a lack of information increases the level of uncertainty and therefore calls for a higher discount rate.

Having evaluated the business plans based on the above criterion, the ice beverage business is more risky than the others are. First, it is based on speculation that a new product in the market will perform and beat established business competitors who offer substitute products. The level of competition is therefore very high. The real estate brokerage might seem more risky based on the initial outlay, but this may be more viable since even the risk of transaction is assumed by the seller and buyer- not the broker. The interstate travel business also requires a substantial amount of finance but it is well-diversified hence reducing other risks (Pierson 2008). For these reasons, the financier is likely to charge a higher discount rate for the ice cream business.

Reference List:

Pratt, S. P. Reilly, R. F. & Schaech R. P. (2000) Valuing a business: the analysis and appraisal of closely held companies: 138 McGraw-Hill Professional,

Hiles A. (2002) Enterprise Risk Assessment and Business Impact Analysis: Best Practices‎ – Rothstein Associates Inc

Pierson G. (2008) Business finance: McGraw-Hill



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