# Present Value Determination and Bond Rating (Math Problem Sample)

Where:

-CO Initial cost of investment

C Cash flow for the period

r Discount rate

n Time or number of periods

Illustration 1. XYZ Company is deciding whether or not they will push through with Project A, considering that they will need to pay $500,000 to initiate the project and that the expected annual cash flows, with 5% discount rate, are as follows:

Year Cash Inflows

1 300,00

2 350,00

3 400,00

Should XYZ Company initiate Project A?

PRESENT VALUE AND BOND RATING

STUDENT NAME:

STUDENT ID:

DATE:

Introduction

Present value of an amount that is to be received in the future can be determined in two major ways. The present value of a lump sum or that of an annuity. The lump sum indicates the present value of an amount paid in one instalment (Denuit, 2008). An amount that is to be received in instalments represents an annuity, which could either be paid in equal instalments or could be unequal depending on the agreement. The current analysis will be based on determination of present value to assess its importance in a current state as well as bond rating of firms.

Present value determination

Present value of an amount has major components including the amount that will be paid which has a future value, the interest rate which is the discounting rate at which the present value will be determined, and time which equals the periods that would be covered for determination of the present value (Johnson, 1986; Grubbström, 1998).

For annuities the present value is given by:

PV = c[1-(1+r/m)-n*m/ r/m]

Where c is the period payment, r is the rate of return, t is the time, and m is the number of payment time in a year

From the information given;

The future value of the amount won= $11,000,000 to be paid in 26 instalment= 11,000,000/26= 423,076.92

Instalment payment periods are equal= 26

Discounting rate per annum= 9%

Compounding is on monthly bases

N= 26

From determination of present value, it will be considered as ordinary annuity as the amount will be expected to be paid at the end of each period.

PV = 423,076.92 [1-(1+0.09/12)-26/ 0.09/12] = $9,960,156.835

The present value determination should be compounded based on time which could be monthly, quarterly, or annually. On this bases, the interest rate need to be apportioned accordingly. From the analysis, the present value of the lottery win is $9,960,156.835. This is the amount that would be given, if it was given immediately. Or after the 26 instalment payments, receive an amount of $11,000,000.

Bond rating

The rating is a standard measure of a company credit quality. Therefore, it is used to measure the strength of a company that is receiving the bonds. Thus, it is used to assess the ability of a firm to make interest on the bond, and its ability to repay the principle bond amount. Therefore, it assesses the likelihood of the debt being repaid (Ederington & Goh, 1998).

It has been realised that bond rating is released by agencies that are licensed to do so. Thus, credit rating is a highly concentrated area with three major firms including; Fitch, Moody, and standard & poor’s (S&P). They have been seen to control over 96% of the ratings. The ratings may fall into 5 major categories including; 1. Financial institutions, brokers, and dealers, 2. Insurance, 3.coporate issuers, 4. Assets-backed securities issuers, 5.issuers of government securities (Sinclair, 2014). The credit rating is given codes which determine the class. The companies publish the codes to assess the risk quality of debt. The codes are AAA, AA, A, BBB, BB, B, CCC, CC, C, and D. The codes are said to be investment grades which are ranked from the strongest to the weakest.

The “A” credit rating is given to high grade. This means that the firms given this code are having very good credit rating and thus their likelihood of repaying interest and the principle bond amount is close to assure. The “AAA” means that a firm has a very strong capacity to meeting its obligation, and “A” indicate a strong repayment capacity. The “B” grade represents a point of speculative. Thus mainly given to non-investment firms. They are able to repay, though have some degree of risk. “BBB” indicates that a firm has adequate capacity to meet its obligations, with “B” meaning that the firm is vulnerable. The “C” rating represent substantial risk. It shows that firm are currently vulnerable and have a high risk of bond repayment. “CCC” means that the firm is currently vulnerable, with “C” meaning that the firm is currently highly vulnerable (Sinclair, 2014). The “D” shows that the firm has in other

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