Question

Global steel prices have a year-over-year inflationary rate increase of 12.4 percent. Tube Fab purchased $700,000 of a particular carbon steel during the year just ended right now, and they intend to purchase the same quantity at the end of each of the next 5 years. Tube Fab earns a real rate of 16 percent on their money.

The following is the cash flow for constant value rate analysis. Determine the constant value amounts they will pay for steel at the end of each of the next 5 years and fill in the correct cash flow below.
The following is the cash flow for Then- current rate analysis. Determine the then-current amounts they will pay for steel at the end of each of the next 5 years and fill in the correct cash flow below.
Determine Tube Fab’s PW of expenditures over the next 5 years using then-current dollars.
Determine Tube Fab’s PW of expenditures over the next 5 years using constant-value dollars.

Answer 1

Constant Value Rate Analysis:

- Year 1: $700,000

- Year 2: $700,000 * 1.124 = $785,680

- Year 3: $700,000 * 1.124^2 = $881,207.63

- Year 4: $700,000 * 1.124^3 = $989,459.54

- Year 5: $700,000 * 1.124^4 = $1,112,098.26

Cash flow for constant value rate analysis:

| Year | Cash Flow |

|------|-----------|

| 1 | -$700,000 |

| 2 | -$785,680 |

| 3 | -$881,207.63 |

| 4 | -$989,459.54 |

| 5 | -$1,112,098.26 |

Then-Current Rate Analysis:

- Year 1: $700,000 * 1.124 = $786,800

- Year 2: $700,000 * 1.124^2 = $883,530.88

- Year 3: $700,000 * 1.124^3 = $992,245.56

- Year 4: $700,000 * 1.124^4 = $1,115,482.59

- Year 5: $700,000 * 1.124^5 = $1,254,174.71

Cash flow for then-current rate analysis:

| Year | Cash Flow |

|------|-----------|

| 1 | -$786,800 |

| 2 | -$883,530.88 |

| 3 | -$992,245.56 |

| 4 | -$1,115,482.59 |

| 5 | -$1,254,174.71 |

To determine Tube Fab's PW of expenditures over the next 5 years using then-current dollars, we need to find the present value of each cash flow using a discount rate of 16%. Using the PV formula, we get:

PW of expenditures using then-current dollars = -$3,420,921.12

To determine Tube Fab's PW of expenditures over the next 5 years using constant-value dollars, we need to find the equivalent constant annual payment (PMT) over the 5-year period. Using the PMT formula, we get:

PMT = -$651,534

Then, we can calculate the PW of these constant payments using a discount rate of 16%. Using the PV formula and summing up the present values of the constant payments, we get:

PW of expenditures using constant-value dollars = -$2,739,073.50