MGT 470 Fall 2015 Test 1 Problem Solutions
4. You are considering leasing a car that cost $35,999. The lease will be for 6 years and requires monthly payments of $300.00.
Somewhere on the lease paperwork you notice a statement to the affect that you will be charged an APR of 3.1800%. What
kind of annuity is this?___________________ What is the implied value of the car at end of the lease (i.e. what is its turn-in
value)? Annuity Due
PV = $35,999
m=12, T=6; n = m x T = 12 x 6 = 72
Solution Opt 1:
rperiodic = rnominal/m = 3.18%/12 = 0.265%;
6 yrs
Set BGN, P/Y=1, N=72, I/Y=0.265, PV=35999, PMT= -300;
CPT FV: $19,729.03
70
71
72
0
1
2
Solution Option 2:
Set BGN, P/Y=12, N=72, I/Y=3.18, PV=35999, PMT= -300;
PMT = $300.00
CPT FV: $19,729.03
Turn-in Value = ?
5. Dick and Jane are both 25 years old and they have decided to start planning for their future financial needs. They have two
children, Sam and Dave. Dick and Jane have decided to start planning for their future financial needs. Their first priority is to
ensure they can finance their sons’ college education. Sam is expected to start college 13 years from now and Dave will start
15 years from now. They assume both sons will attend college for 4 years.
It is 1 January. Starting this month, they plan to contribute a certain amount of money each month (at the beginning of the
month) into an investment account that pays 8.5% APR. They estimate that by the time Sam starts college, the annual cost of
college will be about $14,000 and it will increase every year thereafter by 3% p.a. How much money will Dick and Jane have
to contribute each month into the account? Assume that the annual cost of college must be accumulated by 31 December each
year of school. (Although tuition is due in August, assume Dick and Jane will be able to settle the college accounts at the end
of the year. i.e. although Sam will start school in August of year 13, the tuition won’t have to be paid until 31 Dec of that year,
the end of Year 13.)
Yr 4 = ?
Yr 3 = ?
Note: C/Y for the college years is 1
Yr 6 = ?
Yr 5 = ?
Yr 1 = ? Yr 2 = ?
Months 0
2
3
13
14
167
168
15
16
17
PV = FV = ?
Pmt = ?
Year
1
2
3
4
5
6
Sons in
Tuition
School
$14,000.00
1
$14,420.00
1
$14,852.60
2
$15,298.18
2
$15,757.12
1
$16,229.84
1
Total Costs @ Beginning of
Total Costs
$14,000.00
$14,420.00
$29,705.20
$30,596.36
$15,757.12
$16,229.84
College Yr 1:
BGN, P/Y=12, N=168, I/Y=8.5, FV=98641.21, CPT PT; PMT = $305.19
1
PV Bgn Yr 1
$14,000.00
$13,290.32
$25,233.24
$23,954.13
$11,369.93
$10,793.58
$98,641.21
18
19 Years
MGT 470 Fall 2015 Test 1 Problem Solutions
7. On 14 October 2014 you bought a $1,000 face value BB+ bond which has a coupon rate of 4.9600% and pays semiannual
coupons. At the time you bought this bond, it was selling at par. You sold this bond on 12 October 2015 when its YTM was
4.3670%. The bond matures on 1 March 2022. What is this bond’s holding period return?
Step 1: Find the sales price of the bond in 2015
SDT = 10.1215 CPN = 4.96 RDT = 03.0122 YLD = 4.367 PRI = 103.2698%
VB = 10 x = 103.2698 = $1,032.70
Step 2: Find capital gains yield
Capital gains yield = (New – Old) / Old = ($1,032.70 - $1000.00) / $1000.00 = 3.2700%
Step 4: Find EAR of the coupon rate EAR rcoupon: Use ICONV: NOM=4.96, C/Y=2, CPT EFF; EAR = 5.0215%
Step 5: Add capital gains yield and EAR rcoupon: 3.2700% + 5.0215% = 8.2915%
2