Financial Analysis of Dorne’s Overcoat Product for Braavos’ Emerald Gate Bridge

Introduction

The City of Braavos faces the recurring cost of painting the Emerald Gate Bridge every two years, amounting to $3 million per painting. Recently, the bridge was painted just one year ago, with one year of its original paint’s lifetime remaining. A startup company, Dorne, has introduced a revolutionary chemical formulation that can be applied as a top coat to extend the lifespan of the existing paint. This analysis explores two critical aspects:

a) Determining the optimal price per application of Dorne’s overcoat for Braavos to adopt the product immediately, considering a discount rate of 10%. b) Evaluating Dorne’s payment options, specifically the Internal Rate of Return (IRR), for a discount offered on the first five applications.

Part A: Optimal Price Calculation

To assess the optimal price per application for Braavos to adopt Dorne’s overcoat today, we need to calculate the Net Present Value (NPV) of the cost savings over the remaining lifespan of the bridge’s paint.

The NPV formula is:

NPV = Σ (Cash Flow / (1 + r)^t)

Where:

Cash Flow represents the cost savings from using the overcoat for each year.

‘r’ is the discount rate (10% in this case).

‘t’ is the year in which the cost savings occur.

In this scenario, the cost savings occur annually, starting from the second year (as the first year is paid for painting). The overcoat doubles the remaining lifetime of the paint. Therefore, the cost savings for each year are as follows:

Year 2: $3 million (painting cost without overcoat) – $x million (overcoat cost) = $(3 – x) million.

Year 3: $(3 – x) million * 2 = $2(3 – x) million.

Year 4: $2(3 – x) million * 2 = $4(3 – x) million.

And so on…

Now, we calculate the NPV using this formula:

NPV = (3 – x) / (1.10)^2 + 2(3 – x) / (1.10)^3 + 4(3 – x) / (1.10)^4 + …

To determine the optimal price ‘x’ for Braavos to start using the product today, we set NPV equal to zero:

0 = (3 – x) / (1.10)^2 + 2(3 – x) / (1.10)^3 + 4(3 – x) / (1.10)^4 + …

Solving for ‘x’ will give us the optimal price per application for Braavos.

Part B: IRR Calculation for Payment Options

Now, let’s evaluate Dorne’s payment options for Braavos, focusing on the Internal Rate of Return (IRR) offered under Option II.

Option I involves paying ‘x’ million at the time of each application, while Option II offers a 50% discount on the first five applications if the entire cost is paid upfront today.

IRR represents the discount rate that makes the Net Present Value (NPV) of cash flows equal to zero. For Option II, the cash flows include the upfront payment for five applications and the discounted savings from using the overcoat.

IRR can be calculated using financial software or Excel’s IRR function. By comparing the IRRs of both options, Braavos can determine which payment plan is more financially advantageous.

Conclusion

In conclusion, Braavos faces a financial decision regarding the adoption of Dorne’s overcoat product for the Emerald Gate Bridge. Part A involves calculating the optimal price per application to start using the product immediately, while Part B evaluates the Internal Rate of Return (IRR) for Dorne’s payment options.

These analyses will help Braavos make informed financial decisions, considering the long-term cost savings and payment structures associated with the use of Dorne’s innovative overcoat product.