Financial Analysis and Calculations Homework Problems

This document offers a comprehensive solution to a finance homework assignment, encompassing a range of financial calculations. The assignment is divided into three parts (A, B, and C), each addressing different aspects of finance. Part A focuses on fundamental concepts such as present value, future value, and yield, with problems involving bond valuation, interest rate calculations, and the effective interest rate. Part B delves into more complex scenarios, including the calculation of present values for multiple cash flows, bond valuation with quarterly compounding, and the determination of payments and yields. Part C explores advanced topics, such as the future value of RRSP deposits, the calculation of an equated date for debt settlement, and the analysis of T-bill yields and loan amortization, demonstrating a strong understanding of time value of money, compounding interest, and financial instruments. The solutions are detailed and provide step-by-step explanations, allowing students to understand the underlying principles and calculations thoroughly.

PART A
1) C/Y, P, Y = 1
N= (120/365)
1/Y = 7%
PV= $ 800
CPT FV = $817.99
2) The formula for yield is shown below.
Yield = [(Selling Price – Purchase Price)/Purchase Price] * 365/Holding period
Let the purchase price be X
4.11 = ((100000-X)/X)*365/200
Solving the above, we get X = $ 97,797.55
3) C/Y, P, Y = 2
N=10.5
1/Y = 8%
PV= $ 600
CPT FV = $905.74
4) Present Value = 7500/(1+(6%/12))108 = $4,376.5
5) FV of note = $ 2,000
Time to maturity = 3 years 6 months or 10.5 quarters
Interest rate = 8% p.a. or 2% per quarter
Amount paid for the note = 2000/(1.0210.5) = $ 1,624.53
6) Let the nominal annual rate of interest be X %

Amount = $ 1,150
Principal = $ 700
Time period = 3 years or 6 half years
1150 = 700*(1+(X%/2))6
Solving the above, we get X = 13.98%
7) Effective interest rate (%) = [(1+(6.3%/12))12 -1]*100 = 6.49%
8) The future value of the annuity can be determined using the following formula.
In the given case, P = $ 150, r= (6/12) = 0.5% per month, n = 5 years or 5*12 = 60 months
Hence, FV of these payments = 150*[(1.005)60-1]/0.005 = $ 10,465.5
Total amount deposited = 150*60 = $ 9,000
Hence, interest earned = 10,465.5 – 9,000 = $ 1,465.50
PART B
1) The present value of two amounts needs to be found here. One was due 5 months ago and
other which is due three months from now.
Interest rate = 8.5% p.a. compounded monthly
Amount due in past
Amount due = $ 450
Time = 5 months
Present value = 450*(1+ (8.5%/12))5 = $ 466.16

Amount due in future
Amount due = $ 800
Time = 3 months
Present value = 800/(1+ (8.5%/12))3 = $783.24
Total payment in the present required to discharge both debts = 466.16 + 783.24 = $ 1,249.4
2) Face value = $ 5,000
Interest = 5% of 5000 = $ 25 per annum
Considering quarterly compounding , the interest would be paid @ $6.25 per quarter
Market required rate = 8% p.a. compounded monthly
Interest rate for three month = (1+ (8%/12))3 -1 = 2.013%
The following payments would be discounted at the above rate to determine the current price
as shown below.
Hence, the value would be $ 4,152.47 as on December 1, 2012.
3) a) Let the amount paid on 25th February be $ X
The present value of all the three payments discounted at the given rate of interest should lead
to $20,000 which is the underlying amount borrowed.
$ 5,000 was paid on November 1
Time from date of borrowing = November 1 – August 12 = 81 days
$ 6,000 was paid on December 15

Time from date of borrowing = December 15 – August 12 = = 125 days
$ X was paid on February 25
Time from date of borrowing = February 25 – August 12 = 197 days
Hence, 20000 = (5000/1.105(81/365) + (6000/1.105(125/365) (X/1.105(197/365)
Solving the above, we get X = $ 9,826.7
b) Amount to be paid in the 6th payment = 20000*(1.105(184/365)) = $ 21,032.42
c) Total amount to be given to credit union for full payment assuming no payment has been
done before for the borrowing = 20000*(1.105(184/365)) = $ 21,032.42
PART C
1) The future value of the payments made into the RRSP deposits at the end of the 10 years is
indicated as follows.
For the last five years, when no new money has been deposited, interest has been earned on
the above amount at the rate of 5.5% p.a. compounded monthly.
Hence, beginning balance in RRIF = 27047.61*(1+ (5.5%/4))20 = $ 35,542.35
2) Total payment made = $ 1,250
Debt due today = $ 600
For the debt of $ 600 which was due four months ago, the amount due would be =
600*(1+(9%/12))4 = $ 618.20
Hence, total debt due in today terms = 600 + 618.20 = $ 1,218.20

For settling, the above debt a payment of $ 1,250 has been made and hence the date would be
in future.
1250 = 1218.20*(1+(9%/12))T
Solving the above, we get T = 3.56 months or 3 months 17 days
Hence the equated date would be 3 months 17 days from today.
3) The formula for yield is shown below.
Yield = [(Selling Price – Purchase Price)/Purchase Price] * 365/Holding period
a) Original yield of T bill = [(100000 – 99362.85)/99,362.85]*(365/91) = 2.57%
b) Yield earned during holding period is 2.72%
Hence, 2.72% = (Selling price - 99362.85)/99,362.85]*(365/42)
Solving the above, we get selling price = $130,462.1
4) The formula for installation is as indicated below.
EMI = P*R*(1+R)N/((1+R)N -1)
EMI = $918.65
Interest = 5% p.a. or (5/12) % or 0.41667% per month
N= 4 years or 48 months
918.65 = P*0.0041667*(1.0041667)48/(1.004166748-1)
Solving the above, we get P = $ 39,890.5