Question

1. FV of a 20-year annuity of $200 i/rate is 5% ii/ rate is 10% (first payment is in one year)
2. PV of a 20-year annuity of $200 i/rate is 5% ii/ rate is 10% (first payment is now)
3. IRR of an investment if you make 5 times your initial investment in 6 years (no intermediary Cash Flows)
4. IRR of an investment if you make 4 times your initial investment in 3 years (no intermediary CF)
5. IRR of an investment if you make 2.5 times your initial investment in 4 years (no intermediary CF)
6. IRR of an investment if you make 0.5 time your initial investment in 2 years (no intermediary CF)
7. IRR of an investment if you make 4 times your initial investment in 2.5 years (no intermediary CF)
8. IRR of an investment if you make 1 time your initial investment in 3 years (no intermediary CF)
9. An EBIT grows from $130.5 M to $404.5 M in 5 years i/ what is its overall growth over the period? ii/ what is its CAGR (i.e. its Compound Annual Growth Rate, also called annualized growth rate)?
10. An EBIT declines from $130.5 M to $44.5 M in 5 years i/ what is its overall decline over the period? ii/ what is its CAGR?

Answer 1

1) FV of ordinary annuity = P*[(1+i)ⁿ - 1]/i

P = Annuity Amount = 200$

n = number of years = 20

i = Interest rate

i) Rate is 5%

FV = 200 [ 1.05²⁰ - 1]/0.05 = $6613.19

ii) rate is 10%

FV = 200 [ 1.10²⁰ - 1]/0.10 = $11455

2) PV of annuity due = P + P [1-(1+r)^-(n-1)]/r

P = Annuity amount = $200

n = number of years = 20 years

r = Rate of Interest

i) Rate is 5%

PV = 200 + 200 [ 1-(1.05)^-19]/0.05 = $2617.06

ii) Rate is 10%

PV = 200 + 200 [ 1-(1.10)^-19]/0.10 = $1872.98

3) IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 5

Number of periods = 6

IRR = 5^1/6 - 1 = 30.77%

4)

IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 4

Number of periods = 3

IRR = 4^1/3 - 1 = 58.74%

5)

IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 2.5

Number of periods = 4

IRR = 2.5^1/4 - 1 = 25.74%

6)

IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 0.5111

Number of periods = 2

IRR = 0.5^1/2 - 1 = -29.29%

7)

IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 4

Number of periods = 2.5

IRR = 4^1/2.5 - 1 = 74.11%

8)

IRR with single cash flow is

IRR = (Expected Cash Flow ÷ Initial Outlay)^{(1/number of periods)} - 1

Expected cash flow = 1

Number of periods = 3

IRR = 1^1/3 - 1 = 0%