BUSN1009 - Quantitative Methods Cheat Sheet Cheat Sheet (DRAFT) by jaydenroberts

"If you get a positive value times a number, You need to shift the decimal to the right as many times as the number specified - If negative move it to the right.

Simple interest formula = S=FV=P(1 plus IK)

Compound interest formula = Sk = P (1 plus i)^k

Sn = P (1 plus I/T)^n
where I is interest
T is frequency of compou­nding per year
K is number of years
N is total number of periods - K T or T K

Deprec­iation Formula = Vo or P = Inital value,
Vk = P (1 - d)^k

1. Q = 24-3 p or p = 8 – Q/3

2. Q = 5p-8 or p = 1.6 + 0.2 Q

3, either 24-3 p = 5 p-8 and p = 4
or 8*Q/3 = 1.6 + 0.2 Q and Q = 12

4. TR = p ∙ Q = 8 Q – Q2/3
MR = 8 – 2 Q/3

5. Max Π → MR = MC
8 – 2Q/3 = Q/3
Q = 8
P = 8 – 8/3 = 5.33

6. Impose p≤ 3 – instead of equili­brium price p = 4
Demand at p = 3 : QD = 24-3(3) = 15
Supply at p = 3 : QS = 5(3) -8 = 7
Excess demand = 15 – 7 = 8

7. AVC = 5 + 3 Q
TVC = (AVC) Q = 5 Q + 3 Q2


8. P = 18 – 3Q, MR = 18 – 6Q
18 – 6Q = 12, Q = 1, p = 15

1. 5 years 1 + r = (FV/PV)1/5
(i) r = 10.38%
(ii) r = 10.47%
(iii) r = 10.51%
(iv) r = 10.52%
(v) r = 10.52%
2. 1 + r = (1 + 0.06/12)8 ∙ (1 + 0.072/12)4
1 + r = (1.005)8 ∙ (1.006)4
1 + r = (1.0407) ∙ (1.0242) = 1.06591
r = 6.59%

For an initial outlay of $1000 the net return is 1,000 (1.067) – 10 = 1,057.
Rate of return 5.7%

For larger outlays, e.g. 10,000. 10,000 (1.067) – 10 = 10,660.
Rate of return 6.6%

3. 2500 = 97 (1 + r)40 Take logs of both sides.
Ln(250­0/97) = 40Ln(1 + r) , or 3.249335 = 40Ln(1 + r), or Ln(1+ r) = 0.0812334
Take the expone­ntial of both sides: 1 + r = 1.084624 and r = 8.4624%
97 (1.0867)40 = 97 (27.822) = 2698.72
Either (i)The rate of return is less than the bond rate or (ii) the $97 would have grown to more than $2,500 hence the purchase wasn’t a good invest­ment.

4. (i) 10,000
(ii) 10,000 (1.08)-2 = 10,000 (0.8573) = 8573.39
(iii) 10,000 (1.08)-10 = 10,000 (0.4632) = 4631.93
5. (i) 1,050 (1.05)-1 = 1000
(ii) 1,108 (1.05)-2 = 1004.99 (*)
(iii) 1,160 (1.05)-3 = 1002.05


6. PV = 10,000 (1.07)-2 + 5,000 (1.07)-3 + 15,000 (1.07)-5
PV = 8,734.39 + 4,081.49 + 10,694.79
PV = 23,510.67

7. 100,000 (1 + i )16 = 125,000
4
(1 + i )16 = 1.25 → 1 + i = (1.25) 1/16 = 1.014044
4 4
i = 0.0562 or 5.62%
OR use logarithms
Ln[(1 + i/4)16] = Ln 1.25 and 16Ln( 1 + i/4) = 0.22314
Ln( 1 + i/4) = 0.0139465 and 1 + i/4 = 1.014044.

8. 15,000 (1 + 0.055)12 k = 30,000
12
(1 + 0.055) 12 k = 2
12
12 k Ln (1 + 0.055) = Ln 2
12
12 k 0.0045728 = 0.69315
k = 12.63 years. About 12 years and 7½ months.

1. Add up PV to get NPV
i = 6% A B
-14,000
9.905.66
5,339.98
1,091.51 -15,000
943.40
5,161.98
11,754,67
NVP (6%): 2,337.14 2,860.05 (*)

i = 9% A B
-14,000
9,633.03
5,050.08
1,003.84 -15,000
917.43
4,881.74
10,810.57

NVP (9%): 1,686.95 (*) 1,609.74


2. Find i such that NVP (i) = 0
NVP (10%) = -15,000 + 909.09 + 4,793.39 + 10,518.41
NVP (10%) = 1,220.89 > 0
NVP (12%) = -15,000 + 892.86 + 4,623.72 + 9,964.92
NVP (12%) = 481.51 > 0
NVP (13%) = -15,000 + 884.96 + 4,542.25 + 9,702.70
NVP (13%) = 129.91 > 0
NVP (14%) = -15,000 + 877.19 + 4,462.91 + 9,449.60
NVP (14%) = -210.29 < 0
Say i is approx­imately i = 13.38%


3. PV = 150 [1 – (1 + 0.052 / 52)-156]
0.052/52

PV = 150 [1-0.8556] = 21,656.12
0.001


4. FV = 150 [(1.00­1)156 - 1]
0.001

FV = 150 [1.16873 - 1] = 25,310.26
0.001

FV = PV (1.001)156
25,310.26 = 21,656.12 (1.16873) = 25,310.27
Almost perfect match.

5. (a) R = 120,000 (0.05/12) = 500
[1 – (1 + 0.05)-120] [1 – 0.60716]
12
R = 1272.79

(b) Outsta­nding Balance: B = 1272.79 [1 – (1 + 0.05) -96]/( 0.05/12)
12


B = 1272.79 [1-0.6709] = 100,536.97
0.05/12


(c) New R = 100,536.97 (0.09/12)
[1 – (1 + 0.09) -96]
12

New R = 100,536.97 (0.0075) = 1472.89
[ 1 – 0.48806]