FINANCIAL MANAGEMENT 7

FinancialManagement

Question1

A= 1,600,000

t= 35 years

r= 4% = 0.04

P= required figure

A= P (1 + r) ^t

Therefore,P = A / ((1 + r) ^t)

P= 1,600,000 / ( (1 + 0.04)^35)

(1+ 0.04)^35 = (1.04)^35 = 3.95

P= 1,600,000 / 3.95

=405,063.30

Thus,she will need to invest 405,063.30 today so as to have 1.6 M after 35years at the provided rate.

Now,if P = 405,063.30 r = 18, and A = 1.6 M t can be found as follows

1,600,000= 405,063.30 ((1 + 0.18) ^t)

t= (ln (1600000 / 405063.30)) / ln (1.18)

=1.374 / 0.166

=8.28 years

Question2

P= $ 17,000

r= 9%

Interestin the first year = 17000 * 0.09 * 1

=1530

Principalin the second year = 17000 + 1530 = 18530

Interestin the second year = 18530 * 0.09 * 1 = 1667.70

Principalin the third year = 18530 + 1667.70 = 20207.70

Interestin the third year = 20207.70 * 0.09 * 1 = 1818.693

Therefore,total amount of interest earned in year three would be (1530 +1667.70 + 1818.693)

=5016.4

Incase the simple interest approach was used, the interest in the thirdyear would be as follows

Interest= 17000 * 0.09 * 3 = 4590

Hence,when interest is compounded, there will be an extra (5016.40 –4590) = $ 426. 4 at the end of year three.

Question3

A= P (1 + r) ^t

A= 180,000

P= 3,500

r= 0.11 per month

180,000= 3,500 (1 + 0.11) ^t

t(in months) = ln (180,000 / 3,500) / ln 1.11

=3.94019 / 0.10436

=37.75575

Timein years = 37.75575 / 12

=3.14631 years

Incase Alex pays 4,000 every month, the time for the repayment of theloan would be as follows

t(months) = ln (180,000 / 4,000) / ln 1.11

=3.80666 / 0.10436

=36.47624

Timein years = 36.47624 / 12

=3.03969 years

Question4

Presentvalue = C / (i – g)

C= 80,000

i= 9%

r= 7 %

Thus,the present value would be = 80,000 / (0.09 – 0.07)

=80,000 / 0.02

=4,000,000

Question5

PV= FV/ (1 + i) ^ n

Giventhat the discount rate is 13%, the following would be the presentvalues for the three options

Presentvalue for investment A

=1000 / (1.13) + 2000 / (1.13) ^2 + 3000 / (1.13) ^3 – 3000 / (1.13)^4 + 4000 / (1.13) ^5

=884.95 + 1588.29 + 2079.15 – 1839.96 + 2171.04

=4883.47

Presentvalue for investment B

=1000 / (1.13) + 1000 / (1.13) ^2 + 1000 / (1.13) ^3 + 1000 / (1.13)^4 + 3000 / (1.13) ^5

=884.95 + 783.15 + 693.05 + 613.32 + 1628.28

=4602.75

Presentvalue for investment C

=5000 / (1.13) + 5000 / (1.13) ^ 2 – 5000 / (1.13) ^3 – 5000 /(1.13) ^4 + 15000 / (1.13) ^5

=4424.78 + 3915.73 – 3465.25 – 3066.59 + 8141.40

=9950.07

Fromthe calculations, option C has the highest present value out of thethree.

References

Berges,S. (2004). *Thecomplete guide to real estate finance for investment properties: Howto analyze any single-family, multifamily, or commercial property*.Hoboken, New Jersey: John Wiley & Sons.

Buetow,G. W., & Fabozzi, F. J. (2000). *Valuationof interest rate swaps & swaptions*.New York: John Wiley and Sons Ltd.

Kieso,D. E., Weygandt, J. J., & Warfield, T. D. (2011). *Intermediateaccounting: Vol. 1*.Hoboken, NJ: John Wiley & Sons.

Needles,B. E., Powers, M., & Crosson, S. V. (2011). *Principlesof accounting*.Mason, Ohio: Cengage Learning.

Stickney,C. P. (2010). *Financialaccounting: An introduction to concepts, methods, and uses*.Mason, OH: South-Western/Cengage Learning.